Question

If θ is the angle between any two vectors $\vec a \ and \ \vec b$ , then $\arrowvert\vec a . \vec b\arrowvert = \arrowvert\vec a * \vec b\arrowvert$ when θ is equal to
(A) 0< θ< $\frac{\pi}{2}$
(B)$\frac{\pi}{4}$
(C)$\frac{\pi}{2}$
(D) π

Answer 1

Now,

If there are two vectors, then there cross product equals,

|a × b| = |a||b|Sinθ

Also, there dot product equals,

|a.b| = |a||b|Cosθ

Now, As per as question, it is given that cross product and dot product are equal, therefore,

|a||b|Cosθ = |a||b|Sinθ

∴ Sinθ = Cosθ

Now, Sine is equal to cosine at an angle of 45°  or π/4.

Hence, Correct option is (B).

Hope it helps.