Question

For what values of a are the two vectors A = 2a i - 2j + a k and B = ai 2aj + 2 k perpendicular

Answer 1

Explanation:

Two vectors are perpendicular if their dot product is zero. For A=⟨a,−2,1⟩ and B=⟨2a,a,−4⟩

A⋅B=2a2−2a−4

Setting this equal to zero presents us with a situation where we have to find the roots of A⋅B .

2a2−2a−4=0

Solving for the roots of the above expression by any method of choice, we find that A and B are perpendicular when

a={−12+5–√2,−12−5–√2}