Question

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

Open in App
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).

Suggest Corrections
0