Question

If $\theta$ is the angle between vectors a and b, and $|a\times b|=|a\cdot b|,$ then $\theta$ is equal to

• A. $0^{\circ }$
• B. ${180}^{\circ }$
• C. ${135}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is D ${45}^{\circ }$

$|a\times b|=|a\cdot b|$
$|a||b|\sin \theta =|a||b|\cos \theta \Rightarrow \sin \theta =\cos \theta$
$\Rightarrow \tan \theta =1\Rightarrow \theta ={45}^0$