Question

If $\overrightarrow{A}\times \overrightarrow{B}=0$ and $\overrightarrow{A}.\overrightarrow{B}=-AB$, then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

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

Answer 1

The correct option is D $\pi$

Since, $\overrightarrow{A}\times \overrightarrow{B}=0$.

It can be written as,

$\left|A\right|\left|B\right|\sin \theta =0$

$\theta =0^{\circ }$, $n\pi$

Since, $\overrightarrow{A}\cdot \overrightarrow{B}=-AB$.

It can be written as,

$\left|A\right|\left|B\right|cos\theta =-AB$

$\theta =\left(2n+1\right)\pi$

Thus, the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\pi$.