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Question

If θ is the angle between any two vectors and , then when θ isequal to (A) 0 (B) (C) (D) π

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Solution

It is given that the angle between two vectors a and b is represented by θ and,

| a b |=| a × b |(1)

The formula for the dot product of vectors a and b is,

a b =| a || b |cosθ

The formula for the cross product of vectors a and b is,

a × b =| a || b |sinθ

The magnitude of a b and a × b is given as,

| a b |=| | a || b |cosθ | =| a || b |cosθ | a × b |=| | a || b |sinθ | =| a || b |sinθ

Substitute these values in equation (1).

| a b |=| a × b | | a || b |cosθ=| a || b |sinθ cosθ=sinθ

The cosine and sine are equal when θ= π 4 .

Thus, the correct option is (B).


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