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Question

Let the vectors and be such that and , then is a unit vector, if the angle between and is (A) (B) (C) (D)

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Solution

The given vectors are a and b such that | a |=3and| b |= 2 3 .

As given a × b is a unit vector. Then the magnitude of ( a × b )=| a × b |=1.

The formula for cross product of a and b is,

a × b =| a || b |sinθ n ^ | a × b |=| | a || b |sinθ n ^ | | a × b |=| a || b |sinθ| n ^ |

Since, | n ^ |=1as n ^ is a unit vector, therefore,

| a × b |=| a || b |sinθ×1 | a × b |=| a || b |sinθ

Substitute the given value of | a |and| b |in the above equation.

1=3× 2 3 sinθ sinθ= 1 2 θ= sin 1 ( 1 2 ) θ= π 4

The angle between the vectors a and b is π 4 .

Therefore, the correct option is (B).


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