MAE101 - Test 3 UPDATED ACTUAL Exam Questions and CORRECT Answers

MAE101 - Test 3 UPDATED ACTUAL Exam
Questions and CORRECT Answers
Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides RP and
RQ. Find the other vertex S. - CORRECT ANSWER - a. None of the other choices is correct



A - CORRECT ANSWER - 10 điểm


Which of the vectors below is orthogonal to both (2, 1, -1) and (-3, -2, 4)? - CORRECT
ANSWER - d. (2, -5, -1)


Find the shortest distance between the pair of nonparallel lines [x y z]T = [1 -1 -1]T+t[2 3 1]T
and [x y z]T = [1 -2 -1]T+t[3 2 2]T . - CORRECT ANSWER - 1 / sqrt(42)


Find the area of the triangle with the following vertices A(1, 1, -1), B(2, 0, 1), C(1, -1, 3). -
CORRECT ANSWER - sqrt 5


Let u = (1, 2, 1); v = (2, 3, 0); w = (0, 1, 0). Find projection of u x v on w. - CORRECT
ANSWER - a. (0, 2, 0)


The volume of the pyramid with vertices (0; 0; 0); (-2; 8; 14); (-6; 7;-3) and (4; 0; 2) is: -
CORRECT ANSWER - b. 70


Let be projection on the line y = 2x followed by reflection in the x-axis and let the vector v = [1
1]T. Find T(v). - CORRECT ANSWER - 3/5 -6/5


Let u = (3, 3, 6), v = (4, 4, 3), w = (-6, 3, 3) and x = (41, 5, 12). We can writex = au + bv +
cw,where a, b, c are numbers. Find b. - CORRECT ANSWER - d. 2

, Which of the following are subspaces of R3?(i) {(x, y, z)| 2x-y+3z=0}(ii) (x, y, z)| xy=0} -
CORRECT ANSWER - The correct answer is: (i) only


Find the dimension of the subspace U = {[x, y, z, t] | x+4y-z = 0; x-2z+ t= 0}. - CORRECT
ANSWER - The correct answer is: 2


Find the dimension of the subspace

H = { [a+2b+2d, c+d, -3a-6b+4c-2d, -c-d] | a, b, c, d in R} - CORRECT ANSWER - The
correct answer is: dim H = 2


Let the set of vectors {u, v, w} in R3 be independent. Which of the followings are true?
(i) {u; v; u-v+w} is also independent.

(ii) {u; v+w; u+v+w} is also independent. - CORRECT ANSWER - The correct answer is: (i)
ony


Let X = [a, b, c]. Let U be the subspace spanned by the orthogonal basis{u = [1, 1, 1], v = [1, -1,
0], w = [1, 1, -2]}.Find the coefficient of u when expressing X as a linear combination of {u, v,
w}. - CORRECT ANSWER - The correct answer is: (a+b+c)/3


Find the dimension of the null space of the matrix

[1 -2 3 -3 -1 / -2 5 -5 4 -4 /-1 3 -2 1 -5 ] - CORRECT ANSWER - The correct answer is: 3


Let A be 4 x 7 matrix that has dim(Null(A)) = 5. Choose the correct statements:(i) A has exactly
5 independent columns(ii) A has exactly 2 independent rows - CORRECT ANSWER - The
correct answer is: (ii)


Which of the following points lie on the line with parametric equations
x = 2+4t; y = 3-7t; z = 5t?

P(10; -11; 10); Q(-2; 4; 5); R(-2; 10; -5) - CORRECT ANSWER - The correct answer is: P
and R