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Question: If a vector \(2\widehat{i} + 3\widehat{j} + 8\widehat{k}\) is perpendicular to the vector \(4\wideha...

If a vector 2i^+3j^+8k^2\widehat{i} + 3\widehat{j} + 8\widehat{k} is perpendicular to the vector 4j^−4i^+αk^4\widehat{j} - 4\widehat{i} + \alpha\widehat{k} then the value of α is

A

1/2

B

– 1/2

C

1

D

– 1

Answer

– 1/2

Explanation

Solution

(2i^+3j^+8k^).(4i^−4j^+αk^)\left( 2\widehat{i} + 3\widehat{j} + 8\widehat{k} \right).\left( 4\widehat{i} - 4\widehat{j} + \alpha\widehat{k} \right) = 0 or

-8 + 12 + 8α = 0 α = - ½