Question

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

• A. $0$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

$\overrightarrow{a}=\overrightarrow{8b},\overrightarrow{c}=\overrightarrow{7b}$

$\therefore \overrightarrow{a}=\frac{\overrightarrow{8C}}{7}$

$cos\theta =\frac{\overrightarrow{a}\overrightarrow{c}}{|a||c|}=\frac{\frac{-8}{7}{c}^2}{\frac{8}{7}{c}^2}=-1$

$\theta =\pi$