Question

Let a=(2,2,-1) and b=(2,-1,s), where both are vectors and s is a real number.
Find s so that a and b are parallel.

Answer 1

for A and B to be parallel, A must be some multiple of B (or the other way around). There are no numbers that when multiplied to A or B, will make them a multiple of the other (due to the first two entries of each vector). Thus, there is no such s.
Another way is take cross products, because two vectors are parallel if they have a cross product of 0. But this cross product always results in a nonzero component in the k direction.

Answer 2

Thank you.