Question

When $\overrightarrow{A}.\overrightarrow{B} = - |A||B|,$then

• A. $\overrightarrow{A}$ and $\overrightarrow{B}$ are perpendicular to each other
• B. $\overrightarrow{A}$ and $\overrightarrow{B}$ act in the same direction
• C. $\overrightarrow{A}$ and $\overrightarrow{B}$ act in the opposite direction
• D. $\overrightarrow{A}$ and $\overrightarrow{B}$ can act in any direction

Answer 1

Answer: (C)

$\overrightarrow{A}$ and $\overrightarrow{B}$ act in the opposite direction

Answer 2

$\overset{\rightarrow}{A}.\overset{\rightarrow}{B} = AB\cos\theta$

In the problem $\overset{\rightarrow}{A}.\overset{\rightarrow}{B} = - AB$i.e. $\cos\theta = - 1$∴ $\theta = 180{^\circ}$

i.e. $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$ acts in the opposite direction.