Question

The angle between vectors $(\overrightarrow{A}\times \overrightarrow{B})$ and $(\overrightarrow{B}\times \overrightarrow{A})$ is

• A. Zero
• B. $\pi$
• C. $\pi /4$
• D. $\pi /2$

Answer 1

The correct option is B $\pi$

Given that,

$\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{B}\times \overrightarrow{A}$

We know that,

$\overrightarrow{A}\times \overrightarrow{B}=-\overrightarrow{B}\times \overrightarrow{A}$

$(\overrightarrow{A}\times \overrightarrow{B})\cdot (\overrightarrow{B}\times \overrightarrow{A})=(\overrightarrow{A}\times \overrightarrow{B})\cdot (-\overrightarrow{A}\times \overrightarrow{B})$

$|\overrightarrow{A}\times \overrightarrow{B}||\overrightarrow{B}\times \overrightarrow{A}|\cos \theta =-(\overrightarrow{A}\times \overrightarrow{B})\cdot (\overrightarrow{A}\times \overrightarrow{B})$

$|\overrightarrow{A}\times \overrightarrow{B}{|}^2\cos \theta =-|\overrightarrow{A}\times \overrightarrow{B}{|}^2$

$\cos \theta =-1$

$\cos \theta =\cos \pi$

$\theta =\pi$

Hence, the angle between $\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{B}\times \overrightarrow{A}$ is $\pi$