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).