, TESTBANK FOR Linear Algebra A Modern Introduction 5th Edition Poole
Important Notes
The file includes the complete test bank, organized chapter by chapter.
A sample of selected pages has been provided for preview.
All available appendices and Excel files (if included in the original resources) are
provided.
We continuously update our files to ensure you receive the latest and most accurate
editions.
New editions are added regularly – stay connected for updates!
⚠️Note on Answer Keys: If the answer key is not included within the chapter
questions, you will find the complete answers and solutions at the end of each
chapter.
✅ Why Buy From Us?
📚 Complete & organized chapter-by-chapter – no missing content, no guessing.
⚡ Instant digital delivery – get your file the moment you pay, no waiting.
📅 Always up to date – we track new editions so you always get the latest version.
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, Linear Algebra: Modern Introduction 5E (Poole) – Test Bank
Chapter 1: Sections 1.0 – 1.4
1. If a = [1, –2, 3], b = [4, 0, 1], c = [2, 1, –3], compute 2a – 3b + 4c.
[Open-ended / short-answer question — no stored answer]
2. What does a small SD in a data set indicate about the data?
a. The data points are spread out over a large range of values.
✓ b. The data points are clustered close together, with little variation.
c. The data points are randomly and evenly distributed.
d. The data points are all identical, with no variation.
3. Which statement best describes the correlation between two data sets with a correlation
coefficient ...
a. An increase in one variable is associated with a decrease in the other, but the relationship is weak.
✓ b. An increase in one variable is associated with a decrease in the other, and the relationship is
moderate.
c. An increase in one variable is associated with an increase in the other, but the relationship is weak.
d. No meaningful relationship exists between the two variables.
4. The SD of the data 2, 4, 6, 8, 10 is approximately:
a. 2.5
✓ b. 3
c. 3.5
d. 4
5. A researcher finds a correlation coefficient of 0.7 between the amount of time spent
studying and exam scores. Which of the following conclusions can be drawn from this result?
a. Studying longer causes higher exam scores.
b. Higher exam scores cause longer study sessions.
✓ c. There is a strong linear relationship between studying and exam scores.
d. 70% of exam scores can be predicted by the amount of time spent studying.
6. Given p = [1, –2, 1], q = [4, –4, 7], find: a. p · qb. ||p - q||c. proj...
[Open-ended / short-answer question — no stored answer]
7. Let ABCDEF be a regular hexagon whose sides are of length 5. If = a and = b, find the
projection o...
[Open-ended / short-answer question — no stored answer]
8. Find the distance between the planes
[Open-ended / short-answer question — no stored answer]
,9. Find the distance between the parallel lines.
[Open-ended / short-answer question — no stored answer]
10. Find the acute angle between the planes
[Open-ended / short-answer question — no stored answer]
11. In a parallelogram ABCD let = a, b. Let M be the point of intersection of the diago...
[Open-ended / short-answer question — no stored answer]
12. Find all solutions of 3x + 5 = 2 in , or show that there are no solutions....
[Open-ended / short-answer question — no stored answer]
13. Final all solutions of 7x = 1 in , or show that there are no solutions....
[Open-ended / short-answer question — no stored answer]
14. Find the check digit that should be appended to the vector u = [2, 5, 6, 4, 5] in if the check
vect...
[Open-ended / short-answer question — no stored answer]
15. Let u = (2, 1) and v = (1, 3) be two vectors in R2. What is the coordinate grid determined by
these vectors?
a. A grid with lines of slope ½ spaced 5 units apart and lines of slope 3 spaced 10 units apart.
✓ b. A grid with lines of slope ½ spaced [image] units apart and lines of slope 3 spaced [image] units apart.
c. A grid with lines of slope ½ spaced 1 unit apart and lines of slope 3 spaced 3 units apart.
d. A grid with lines of slope ½ spaced 2 units apart and lines of slope 3 spaced 3 units apart.
16. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w u)....
[Open-ended / short-answer question — no stored answer]
17. . Given the vectors a = [–1, 2, 0], b = [–1, 1, 1], c = [ 3, 0 1], the first component of the vector
v = a 2b + c is:
a. –2
b. 0
✓ c. 2
d. 4
18. In a triangle ABC, let K be the midpoint of the side , and let M be the midpoint of . Let p =
and ...
a. [image] (p + q)
b. [image] p – [image] p
c. [image] (p – q)
✓ d. [image] (p– q)
19. Given a = [2, 3, 0], b = [0, –3, –2], then the orthogonal projection of a + b along [0, ...
✓ a. [0, –2, –2]
b. [2, 0, –2]
, c. [0, 6, 0]
d. [0, 2, –2]
20. If a = [1, 3, z], b = [x, –6, 2], then a and b are collinear vectors if:
a. x = 2, z = 1
✓ b. x = –2, z = –1
c. x = –1, z = 2
d. x = 1, z = 2
21. Suppose || p || = 3 and || q || = 5. Then the vectors p + kq and p – kq are orthogonal if:...
a. [image]
b. [image]
c. [image]
✓ d. [image]
22. Suppose that the dot product of two vectors in were defined as the product of the lengths
of the ve...
a. u ■ v = v ■ u
b. u ■ u ≥ 0
✓ c. u ■ (v + w) = u ■ v + u ■ w
d. [image]
23. If u1 and u2 are unit vectors and a = u1 + 2u2 is perpendicular to b = 5u1 – 4u2, then the
ang...
a. [image]
✓ b. [image]
c. [image]
d. [image]
24. Which of the following is not true for all vectors u, v?...
✓ a. ||u – v|| ≤ ||u|| – ||v||
b. ||u + v||2 + ||u – v||2 = 2||u||2 + 2||v||2
c. u ■ v = [image]
d. |u ■ v| ≤ ||u|| ||v||
25. For all vectors v in , the nonzero vector u is orthogonal to:...
a. proju (v)
b. projv (u)
c. v + proju (v)
✓ d. v – proju (v)
26. Which of the following expresses the fact that the vectors u and v have the same length?
a. ||u + v|| = ||u|| – ||v||
b. ||u + v|| = ||u|| + ||v||
✓ c. u ■ u = v ■ v
, d. [image]
27. Solve for the vector x in terms of a and b: 2x - a = 3b = 2(a + b) - (x - b).
[Open-ended / short-answer question — no stored answer]
28. The vector form of the equation of the line in through P = (2, 0, –3) and parallel to the lin...
a. [image]
✓ b. [image]
c. [image]
d. [image]
29. The equation of the plane that is equidistant from the two planes 5x – 3y + z = –3 and 10x –
6y + 2z = –7 is:
a. [image]
b. [image]
c. [image]
✓ d. [image]
30. Let L be the line with parametric equations x = 1 + 2t, y = t, z = –1. The distance from L to ...
a. [image]
b. [image]
✓ c. [image]
d. [image]
31. The distance between the two planes 2x – y + z = 1 and –4x + 2y – 2z = 1 is:
✓ a. [image]
b. [image]
c. [image]
d. [image]
32. Which of the following equations has no solution?
a. 7x = 1 in [image]
b. 3x + 5 = 2 in [image]
✓ c. 6x = 2 in [image]
d. 7x + 1 = 2 in [image]
33. What digit should be appended to the vector u = [2, 5, 6, 4, 5] in if the check vector is:
a. 5
✓ b. 6
c. 4
d. 3
34. A certain check digit code uses the check vector c = [9, 8, 7, 6, 5, 4, 3, 2, 1] and appends a
ninth...
a. 4
, ✓ b. 5
c. 6
d. 7
35. Which of the following is not equal to a ? b × c for all a, b, c in 3?...
a. b ■ c × a
b. c ■ a × b
c. –b × a ■ c
✓ d. b ■ a × c
36. Suppose that three vectors satisfy a + 2b + c = 0. Which of the following is equal to a × b?
a. c × b
b. a × c
c. [image] (a × c)
✓ d. [image] (c × a)
37. The cosine of the angle between the planes x + 2y – z + 1 = 0 and –x + 3z + 1 = 0 is:...
a. [image]
b. [image]
✓ c. [image]
d. [image]
38. Find values of the scalar k for which the following vectors are orthogonal.
[Open-ended / short-answer question — no stored answer]
39. If v is any nonzero vector, then 6v is a vector in the same direction as v with a length of 6
units.
a. True
✓ b. False
40. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
a. True
✓ b. False
41. Let u = (3,2) and v = (1,4) be two vectors in 2 Which of the following best describes the
coord...
✓ a. A grid with lines of slope 2/3 intersecting lines of slope 4 at 45-degree angles.
b. A grid with lines of slope 2/3 parallel to lines of slope 4.
c. A grid with lines of slope 2/3 perpendicular to lines of slope 4.
d. A grid with lines of slope 2/3 intersecting lines of slope 4 at 90-degree angles.
42. If u • v = u • w, then either u = 0 or v = w....
a. True
✓ b. False
43. The only real number c for which [c, –2, 1] is orthogonal to [2c, c, –4] is c = 2....
, a. True
✓ b. False
44. The distance between two points in
✓ a. True
b. False
45. The zero vector is orthogonal to every vector except itself.
a. True
✓ b. False
46. The projection of a vector v onto a vector u is undefined if v = 0....
a. True
✓ b. False
47. The projection of a vector v onto a vector u is undefined if u = 0.
✓ a. True
b. False
48. The projection of vector v onto vector u is equal to v if:
a. u and v are orthogonal
b. u = 0
c. v = 0
✓ d. u and v are parallel
49. If u is orthogonal to v, then which of the following is also orthogonal to v?
[Open-ended / short-answer question — no stored answer]
50. The length of the projection of vector u onto vector v is:
✓ a. less than or equal to length of u
b. greater than or equal to length of u
c. equal to length of v
d. equal to length of u
51. The distance between the planes n • x = d1 and n • x = d2 is |d1 – d2|....
a. True
✓ b. False
52. The area of the parallelogram with sides a and b with |a| = 3 and |b| = 4 is 6. What is the
angle between vectors a and b?
✓ a. 30°
b. 45°
c. 60°
d. 90°
53. a • b × c = 0 if and only if the vectors a, b, c are coplanar.
, ✓ a. True
b. False
54. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
a. True
✓ b. False
55. If a, b, c are mutually orthogonal vectors in R^3, then (a × b • c)2 = ||a||2||b||2||c||2.
✓ a. True
b. False
56. If a parity check code is used in the transmission of a message consisting of a binary
vector, then the total number of 1’s in the message will be even.
✓ a. True
b. False
57. If u • v = 0, then ||u + v|| = ||u – v||....
✓ a. True
b. False
58. For all vectors u, v, w in n, u – (v – w) = u + w – v....
✓ a. True
b. False
59. For all vectors v and scalars c, ||cv|| = c||v||.
✓ a. True
b. False
60. Find all values of k such that d(a, b) = 6, where a = [2, k, 1, –4] and b = [3, –1, 6, –3].
[Open-ended / short-answer question — no stored answer]
61. The area of the parallelogram with sides a, b, is
✓ a. True
b. False
62. Given the vectors a = [–1, 2, 1], b = [3, 1, 1], c = [4, 3, 0], the orthogonal projection of 2...
✓ a. [image]
b. [image]
c. [–164, –123, 0]
d. [11, –1,1]
63. The angle between u = [–1, 2, 0] and e2 = [0, 1, 0] is:
✓ a. acute
b. obtuse
c. 90°
d. 0°
, 64. Which of the following vectors x is collinear with a = [2, 1, –1] and satisfies the condition a
? x = 3?
✓ a. [image]
b. [1, 1, 0]
c. [image]
d. [image]
65. The distance from the point Q = (l, l) to the line
✓ a. [image]
b. 3
c. [image]
d. [image]
66. The equation of the plane in 3 passing through the points P = (1, 2, 0), Q = (2, 1, 1) and
parallel ...
✓ a. –x + 2y – 3z = 3
b. x + 2y + 3z = –3
c. x – 2y – 3z = 3
d. x – 2y + 3z = –3
67. Find a unit vector in 3 in the opposite direction to v = [1, 2, –2]....
[Open-ended / short-answer question — no stored answer]
68. Find the vector parametric equation of the line in 3 that is perpendicular to the plane 2x –
3...
[Open-ended / short-answer question — no stored answer]
69. Show that the quadrilateral with vertices A = (–3, 5, 6), B = (1, –5, 7), C = (8, –3, –1) and D =
(4, 7, –2) is a square.
[Open-ended / short-answer question — no stored answer]
70. Find a value of k so that the angle between the line 4x + ky = 20 and the line 2x – 3y =
&ndas...;
[Open-ended / short-answer question — no stored answer]
71. Suppose that the dot product of u = [u1, u2] and v = [v1, v2] in R2 were defined as u • v =
5u_1 v_1 + 2u_2 v_2. Consider the following statements for vectors u, v, w, and all scalars c.
[Open-ended / short-answer question — no stored answer]
72. What is the distance of the point P = (2, 3, –1) to the line of intersection of the planes 2x ...
[Open-ended / short-answer question — no stored answer]
73. Let u1 and u2 be unit vectors, and let the angle between them be radians. What is the area
of the p...
[Open-ended / short-answer question — no stored answer]
Important Notes
The file includes the complete test bank, organized chapter by chapter.
A sample of selected pages has been provided for preview.
All available appendices and Excel files (if included in the original resources) are
provided.
We continuously update our files to ensure you receive the latest and most accurate
editions.
New editions are added regularly – stay connected for updates!
⚠️Note on Answer Keys: If the answer key is not included within the chapter
questions, you will find the complete answers and solutions at the end of each
chapter.
✅ Why Buy From Us?
📚 Complete & organized chapter-by-chapter – no missing content, no guessing.
⚡ Instant digital delivery – get your file the moment you pay, no waiting.
📅 Always up to date – we track new editions so you always get the latest version.
💬 Friendly support – real humans ready to help, anytime you need us.
🔒 Safe & secure – thousands of satisfied students trust us every semester.
🛡️Our Guarantees
💰 Money-Back Guarantee: Not satisfied? We offer a full refund – no questions asked.
🔄 Wrong File? No Problem: Contact us and we will replace it immediately with the
correct version, free of charge.
⏰ 24/7 Support: We are always here – reach out anytime and expect a fast response.
Contact Email:
, Linear Algebra: Modern Introduction 5E (Poole) – Test Bank
Chapter 1: Sections 1.0 – 1.4
1. If a = [1, –2, 3], b = [4, 0, 1], c = [2, 1, –3], compute 2a – 3b + 4c.
[Open-ended / short-answer question — no stored answer]
2. What does a small SD in a data set indicate about the data?
a. The data points are spread out over a large range of values.
✓ b. The data points are clustered close together, with little variation.
c. The data points are randomly and evenly distributed.
d. The data points are all identical, with no variation.
3. Which statement best describes the correlation between two data sets with a correlation
coefficient ...
a. An increase in one variable is associated with a decrease in the other, but the relationship is weak.
✓ b. An increase in one variable is associated with a decrease in the other, and the relationship is
moderate.
c. An increase in one variable is associated with an increase in the other, but the relationship is weak.
d. No meaningful relationship exists between the two variables.
4. The SD of the data 2, 4, 6, 8, 10 is approximately:
a. 2.5
✓ b. 3
c. 3.5
d. 4
5. A researcher finds a correlation coefficient of 0.7 between the amount of time spent
studying and exam scores. Which of the following conclusions can be drawn from this result?
a. Studying longer causes higher exam scores.
b. Higher exam scores cause longer study sessions.
✓ c. There is a strong linear relationship between studying and exam scores.
d. 70% of exam scores can be predicted by the amount of time spent studying.
6. Given p = [1, –2, 1], q = [4, –4, 7], find: a. p · qb. ||p - q||c. proj...
[Open-ended / short-answer question — no stored answer]
7. Let ABCDEF be a regular hexagon whose sides are of length 5. If = a and = b, find the
projection o...
[Open-ended / short-answer question — no stored answer]
8. Find the distance between the planes
[Open-ended / short-answer question — no stored answer]
,9. Find the distance between the parallel lines.
[Open-ended / short-answer question — no stored answer]
10. Find the acute angle between the planes
[Open-ended / short-answer question — no stored answer]
11. In a parallelogram ABCD let = a, b. Let M be the point of intersection of the diago...
[Open-ended / short-answer question — no stored answer]
12. Find all solutions of 3x + 5 = 2 in , or show that there are no solutions....
[Open-ended / short-answer question — no stored answer]
13. Final all solutions of 7x = 1 in , or show that there are no solutions....
[Open-ended / short-answer question — no stored answer]
14. Find the check digit that should be appended to the vector u = [2, 5, 6, 4, 5] in if the check
vect...
[Open-ended / short-answer question — no stored answer]
15. Let u = (2, 1) and v = (1, 3) be two vectors in R2. What is the coordinate grid determined by
these vectors?
a. A grid with lines of slope ½ spaced 5 units apart and lines of slope 3 spaced 10 units apart.
✓ b. A grid with lines of slope ½ spaced [image] units apart and lines of slope 3 spaced [image] units apart.
c. A grid with lines of slope ½ spaced 1 unit apart and lines of slope 3 spaced 3 units apart.
d. A grid with lines of slope ½ spaced 2 units apart and lines of slope 3 spaced 3 units apart.
16. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w u)....
[Open-ended / short-answer question — no stored answer]
17. . Given the vectors a = [–1, 2, 0], b = [–1, 1, 1], c = [ 3, 0 1], the first component of the vector
v = a 2b + c is:
a. –2
b. 0
✓ c. 2
d. 4
18. In a triangle ABC, let K be the midpoint of the side , and let M be the midpoint of . Let p =
and ...
a. [image] (p + q)
b. [image] p – [image] p
c. [image] (p – q)
✓ d. [image] (p– q)
19. Given a = [2, 3, 0], b = [0, –3, –2], then the orthogonal projection of a + b along [0, ...
✓ a. [0, –2, –2]
b. [2, 0, –2]
, c. [0, 6, 0]
d. [0, 2, –2]
20. If a = [1, 3, z], b = [x, –6, 2], then a and b are collinear vectors if:
a. x = 2, z = 1
✓ b. x = –2, z = –1
c. x = –1, z = 2
d. x = 1, z = 2
21. Suppose || p || = 3 and || q || = 5. Then the vectors p + kq and p – kq are orthogonal if:...
a. [image]
b. [image]
c. [image]
✓ d. [image]
22. Suppose that the dot product of two vectors in were defined as the product of the lengths
of the ve...
a. u ■ v = v ■ u
b. u ■ u ≥ 0
✓ c. u ■ (v + w) = u ■ v + u ■ w
d. [image]
23. If u1 and u2 are unit vectors and a = u1 + 2u2 is perpendicular to b = 5u1 – 4u2, then the
ang...
a. [image]
✓ b. [image]
c. [image]
d. [image]
24. Which of the following is not true for all vectors u, v?...
✓ a. ||u – v|| ≤ ||u|| – ||v||
b. ||u + v||2 + ||u – v||2 = 2||u||2 + 2||v||2
c. u ■ v = [image]
d. |u ■ v| ≤ ||u|| ||v||
25. For all vectors v in , the nonzero vector u is orthogonal to:...
a. proju (v)
b. projv (u)
c. v + proju (v)
✓ d. v – proju (v)
26. Which of the following expresses the fact that the vectors u and v have the same length?
a. ||u + v|| = ||u|| – ||v||
b. ||u + v|| = ||u|| + ||v||
✓ c. u ■ u = v ■ v
, d. [image]
27. Solve for the vector x in terms of a and b: 2x - a = 3b = 2(a + b) - (x - b).
[Open-ended / short-answer question — no stored answer]
28. The vector form of the equation of the line in through P = (2, 0, –3) and parallel to the lin...
a. [image]
✓ b. [image]
c. [image]
d. [image]
29. The equation of the plane that is equidistant from the two planes 5x – 3y + z = –3 and 10x –
6y + 2z = –7 is:
a. [image]
b. [image]
c. [image]
✓ d. [image]
30. Let L be the line with parametric equations x = 1 + 2t, y = t, z = –1. The distance from L to ...
a. [image]
b. [image]
✓ c. [image]
d. [image]
31. The distance between the two planes 2x – y + z = 1 and –4x + 2y – 2z = 1 is:
✓ a. [image]
b. [image]
c. [image]
d. [image]
32. Which of the following equations has no solution?
a. 7x = 1 in [image]
b. 3x + 5 = 2 in [image]
✓ c. 6x = 2 in [image]
d. 7x + 1 = 2 in [image]
33. What digit should be appended to the vector u = [2, 5, 6, 4, 5] in if the check vector is:
a. 5
✓ b. 6
c. 4
d. 3
34. A certain check digit code uses the check vector c = [9, 8, 7, 6, 5, 4, 3, 2, 1] and appends a
ninth...
a. 4
, ✓ b. 5
c. 6
d. 7
35. Which of the following is not equal to a ? b × c for all a, b, c in 3?...
a. b ■ c × a
b. c ■ a × b
c. –b × a ■ c
✓ d. b ■ a × c
36. Suppose that three vectors satisfy a + 2b + c = 0. Which of the following is equal to a × b?
a. c × b
b. a × c
c. [image] (a × c)
✓ d. [image] (c × a)
37. The cosine of the angle between the planes x + 2y – z + 1 = 0 and –x + 3z + 1 = 0 is:...
a. [image]
b. [image]
✓ c. [image]
d. [image]
38. Find values of the scalar k for which the following vectors are orthogonal.
[Open-ended / short-answer question — no stored answer]
39. If v is any nonzero vector, then 6v is a vector in the same direction as v with a length of 6
units.
a. True
✓ b. False
40. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
a. True
✓ b. False
41. Let u = (3,2) and v = (1,4) be two vectors in 2 Which of the following best describes the
coord...
✓ a. A grid with lines of slope 2/3 intersecting lines of slope 4 at 45-degree angles.
b. A grid with lines of slope 2/3 parallel to lines of slope 4.
c. A grid with lines of slope 2/3 perpendicular to lines of slope 4.
d. A grid with lines of slope 2/3 intersecting lines of slope 4 at 90-degree angles.
42. If u • v = u • w, then either u = 0 or v = w....
a. True
✓ b. False
43. The only real number c for which [c, –2, 1] is orthogonal to [2c, c, –4] is c = 2....
, a. True
✓ b. False
44. The distance between two points in
✓ a. True
b. False
45. The zero vector is orthogonal to every vector except itself.
a. True
✓ b. False
46. The projection of a vector v onto a vector u is undefined if v = 0....
a. True
✓ b. False
47. The projection of a vector v onto a vector u is undefined if u = 0.
✓ a. True
b. False
48. The projection of vector v onto vector u is equal to v if:
a. u and v are orthogonal
b. u = 0
c. v = 0
✓ d. u and v are parallel
49. If u is orthogonal to v, then which of the following is also orthogonal to v?
[Open-ended / short-answer question — no stored answer]
50. The length of the projection of vector u onto vector v is:
✓ a. less than or equal to length of u
b. greater than or equal to length of u
c. equal to length of v
d. equal to length of u
51. The distance between the planes n • x = d1 and n • x = d2 is |d1 – d2|....
a. True
✓ b. False
52. The area of the parallelogram with sides a and b with |a| = 3 and |b| = 4 is 6. What is the
angle between vectors a and b?
✓ a. 30°
b. 45°
c. 60°
d. 90°
53. a • b × c = 0 if and only if the vectors a, b, c are coplanar.
, ✓ a. True
b. False
54. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
a. True
✓ b. False
55. If a, b, c are mutually orthogonal vectors in R^3, then (a × b • c)2 = ||a||2||b||2||c||2.
✓ a. True
b. False
56. If a parity check code is used in the transmission of a message consisting of a binary
vector, then the total number of 1’s in the message will be even.
✓ a. True
b. False
57. If u • v = 0, then ||u + v|| = ||u – v||....
✓ a. True
b. False
58. For all vectors u, v, w in n, u – (v – w) = u + w – v....
✓ a. True
b. False
59. For all vectors v and scalars c, ||cv|| = c||v||.
✓ a. True
b. False
60. Find all values of k such that d(a, b) = 6, where a = [2, k, 1, –4] and b = [3, –1, 6, –3].
[Open-ended / short-answer question — no stored answer]
61. The area of the parallelogram with sides a, b, is
✓ a. True
b. False
62. Given the vectors a = [–1, 2, 1], b = [3, 1, 1], c = [4, 3, 0], the orthogonal projection of 2...
✓ a. [image]
b. [image]
c. [–164, –123, 0]
d. [11, –1,1]
63. The angle between u = [–1, 2, 0] and e2 = [0, 1, 0] is:
✓ a. acute
b. obtuse
c. 90°
d. 0°
, 64. Which of the following vectors x is collinear with a = [2, 1, –1] and satisfies the condition a
? x = 3?
✓ a. [image]
b. [1, 1, 0]
c. [image]
d. [image]
65. The distance from the point Q = (l, l) to the line
✓ a. [image]
b. 3
c. [image]
d. [image]
66. The equation of the plane in 3 passing through the points P = (1, 2, 0), Q = (2, 1, 1) and
parallel ...
✓ a. –x + 2y – 3z = 3
b. x + 2y + 3z = –3
c. x – 2y – 3z = 3
d. x – 2y + 3z = –3
67. Find a unit vector in 3 in the opposite direction to v = [1, 2, –2]....
[Open-ended / short-answer question — no stored answer]
68. Find the vector parametric equation of the line in 3 that is perpendicular to the plane 2x –
3...
[Open-ended / short-answer question — no stored answer]
69. Show that the quadrilateral with vertices A = (–3, 5, 6), B = (1, –5, 7), C = (8, –3, –1) and D =
(4, 7, –2) is a square.
[Open-ended / short-answer question — no stored answer]
70. Find a value of k so that the angle between the line 4x + ky = 20 and the line 2x – 3y =
&ndas...;
[Open-ended / short-answer question — no stored answer]
71. Suppose that the dot product of u = [u1, u2] and v = [v1, v2] in R2 were defined as u • v =
5u_1 v_1 + 2u_2 v_2. Consider the following statements for vectors u, v, w, and all scalars c.
[Open-ended / short-answer question — no stored answer]
72. What is the distance of the point P = (2, 3, –1) to the line of intersection of the planes 2x ...
[Open-ended / short-answer question — no stored answer]
73. Let u1 and u2 be unit vectors, and let the angle between them be radians. What is the area
of the p...
[Open-ended / short-answer question — no stored answer]
