Question

If $a$ and $b$ are two vectors, such that $a.b<0$ and $|a.b|=|a\times b|$, then the angle between vectors $a$ and $b$ is

• A. $\pi$
• B. $\frac{7\pi }{4}$
• C. $\frac{\pi }{4}$
• D. $\frac{3\pi }{4}$

Answer 1

The correct option is D $\frac{3\pi }{4}$

We have $|a.b|=|a\times b|$

$\Rightarrow \left|a\right|\left|b\right|\left|\cos \theta \right|=\left|a\right|\left|b\right|\left|\sin \theta \right|$

$($ where $\theta$ is the angle between $a$ and $b)$

$\Rightarrow \left|\cos \theta \right|=\left|\sin \theta \right|\Rightarrow \theta =\frac{\pi }{4}$ or $\frac{3\pi }{4}$

But $a.b<0,\therefore \theta =\frac{3\pi }{4}$