Question

you are given the vectors p=(2,-2,-3) and q=(a,b,6).
a. determine the values of a and b is q is collinear with p.
b. determine an algebraic condition for p and q to be perpendicular.
c. using the answer from part b., determine the components of a unit vector that is perpendicular to p.

Answer 1

(a) q must be a multiple of p. Since 6/-3 = -2, that multiple is ±2
(b) p•q = 0
(c) if r = p×q, then you want r/|r|