Question

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

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

Answer 1

Answer: (D)

$\frac{3\pi }{4}$

Given, $|a.b|=|a\times b|$
$|\overline{a}||\overline{b}||\cos \theta |=|\overline{a}||\overline{b}||\sin \theta |$
(where $\theta$ is angle between $\overline{a}$ and $\overline{b}$)
$\Rightarrow |\cos \theta |=|\sin \theta |$
$\theta =\frac{\pi }{4}$ or $\frac{3\pi }{4}$ (as $0\le \theta \le \pi$)
But $\overline{a}.\overline{b}<0$
$\therefore \theta =\frac{3\pi }{4}$