Question

The non-zero vectors $\underset{a}{\overset{}{\to }},\underset{b}{\overset{}{\to }}$ and $\underset{c}{\overset{}{\to }}$ are related by $\underset{a}{\overset{}{\to }}=8\underset{b}{\overset{}{\to }}$ and $\underset{c}{\overset{}{\to }}=-7\underset{b}{\overset{}{\to }}$. Then, the angle between $\underset{a}{\overset{}{\to }}$ and $\underset{c}{\overset{}{\to }}$ is-

• A. 0
• B. $\underset{\pi }{\overset{4}{\to }}$
• C. $\underset{\pi }{\overset{2}{\to }}$
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

$\stackrel{\overrightarrow{b}}{\to }$

$\overrightarrow{a}=8\overrightarrow{b}$ [Direction is same but magnitude is 8 times]

So $\underset{\overrightarrow{a}=8\overrightarrow{b}}{\overset{}{\to }}$

$\overrightarrow{c}=-7\overrightarrow{b}$

$\underset{\overrightarrow{a}=-7\overrightarrow{b}}{\overset{}{\leftarrow }}$

$anglebetween\overrightarrow{a}\&\overrightarrow{b}is,So$

$D^{\prime }Rissameboth\overrightarrow{a}\&\overrightarrow{b}$

$anglebetween\overrightarrow{a}\&\overrightarrow{b}=0$

$anglebetween\overrightarrow{a}\&\overrightarrow{c}=\pi$

Because It is in opposite direction.