Question

If $\vec{a}$ and $\vec{b}$ are two vectors, such that $\vec{a}\cdot \vec{b}<0$ and $|\vec{a}\cdot \vec{b}|=|\vec{a}\times \vec{b}|$, then angle between vectors $\vec{a}$ and $\vec{b}$ is

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

Answer 1

Answer: (D)

$|\vec{a}\cdot \vec{b}|=|\vec{a}\times \vec{b}|$
$|\vec{a}||\vec{b}|\cos \pi |=|\vec{a}||\vec{b}||\sin \theta \mid$
(where $\theta$ is angle between $\vec{a}$ and $\vec{b}$ )
$\Rightarrow |\cos \theta |=|\sin \theta |$
$\Rightarrow \theta =\frac{\pi }{4}$ or $\frac{3\pi }{4}($ as $0\le \theta \le T\le \pi )$
But $\vec{a}\cdot \vec{b}<0$
$\therefore \theta =\frac{3\pi }{4}$