If θ is the angle between any two vectors and , then when θ isequal to (A) 0 (B) (C) (D) π
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 → | cos θ
The formula for the cross product of vectors a → and b → is,
a → × b → = | a → | | b → | sin θ
The magnitude of a → ⋅ b → and a → × b → is given as,
| a → ⋅ b → | = | | a → | | b → | cos θ | = | a → | | b → | cos θ | a → × b → | = | | a → | | b → | sin θ | = | a → | | b → | sin θ
Substitute these values in equation (1).
| a → ⋅ b → | = | a → × b → | | a → | | b → | cos θ = | a → | | b → | sin θ cos θ = sin θ
The cosine and sine are equal when θ = π 4 .
Thus, the correct option is (B).
It is given that the angle between two vectors
The formula for the dot product of vectors
The formula for the cross product of vectors
The magnitude of
Substitute these values in equation (1).
The cosine and sine are equal when
Thus, the correct option is (B).
and
,
then
when
θisequal
to
(C) 
(D) π