Question

If θ is the angle between any two vectors $\vec a$ and $\vec b$ , then|$\vec a.\vec b$|=|$\vec a \times \vec b$| when θ is equal to

Answer 1

Let θ be the angle between two vectors $\vec a$ and $\vec b$.
Then, without loss of generality,$\vec a$and $\vec b$are non-zero vectors,so
that |$\vec a$|and |$\vec b$|are positive.
|$\vec a.\vec b$|=|$\vec a \times \vec b$|
⇒ |$\vec a$||$\vec b$|cosθ=$\vec a$||$\vec b$|sinθ
⇒ cosθ=sinθ [|$\vec a$|and|$\vec b$|are positive]
⇒ tanθ=1
⇒ θ=$\frac{\pi}{4}$
Hence,|$\vec a.\vec b$|=|$\vec a \times \vec b$|when θ=$\frac{\pi}{4}$
The correct answer is B.