MAT232 FINAL COMPLETE STUDY GUIDE WITH
SOLVED QUESTIONS
◉ magnitude of a vector.
Answer:
◉ unit vector.
Answer:
◉ standard basis vectors.
Answer: i=<1,0,0>, k=<0,1,0>, j=<0,0,1>
◉ two vectors are orthogonal if.
Answer: their dot product = 0
◉ two vectors are parallel if.
Answer: their cross product = 0
◉ angle between two vectors v and w.
Answer:
, ◉ projection of u onto v.
Answer:
◉ comp of b along a.
Answer: (a•b)/ ll a ll
◉ area of a parallelogram with lengths a, b.
Answer: ll a x b ll
◉ volume of parallelepiped determined by a, b, c.
Answer: ll a • (b x c) ll
◉ torque.
Answer: magnitude of
◉ unit tangent vector.
Answer:
◉ arc length formula.
Answer: integral from a to b of |r'(t)| dt
◉ curvature.
SOLVED QUESTIONS
◉ magnitude of a vector.
Answer:
◉ unit vector.
Answer:
◉ standard basis vectors.
Answer: i=<1,0,0>, k=<0,1,0>, j=<0,0,1>
◉ two vectors are orthogonal if.
Answer: their dot product = 0
◉ two vectors are parallel if.
Answer: their cross product = 0
◉ angle between two vectors v and w.
Answer:
, ◉ projection of u onto v.
Answer:
◉ comp of b along a.
Answer: (a•b)/ ll a ll
◉ area of a parallelogram with lengths a, b.
Answer: ll a x b ll
◉ volume of parallelepiped determined by a, b, c.
Answer: ll a • (b x c) ll
◉ torque.
Answer: magnitude of
◉ unit tangent vector.
Answer:
◉ arc length formula.
Answer: integral from a to b of |r'(t)| dt
◉ curvature.
