Question

A vector= ai+2j-k, B vector =2ai-aj+4k
Find value of a

Answer 1

Answer:

For what value of ‘a’ are A= ai-2j+k and B= 2ai+aj-4k perpendicular?

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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}