Q. The non-zero vectors $\overrightarrow{\mathbf{a}}\ ,\overrightarrow{\mathbf{b}}\ and\ \overrightarrow{\mathbf{c}}$ are related by $\overrightarrow{\mathbf{a}} = 8\overrightarrow{\mathbf{b}}\ and\ \overrightarrow{\mathbf{c}} = - 7\overrightarrow{\mathbf{b}}.$Then, the angle between $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{c}}$ is
A) $\pi$
B) 0
C) $\frac{\pi}{4}$
D) $\frac{\pi}{2}$
Explanation
(a)
Since, $\overrightarrow{\mathbf{a}} = 8\overrightarrow{\mathbf{b}}\ and\ \overrightarrow{\mathbf{c}} = - 7\overrightarrow{\mathbf{b}}$
$\therefore\ \overrightarrow{\mathbf{a}}$ is parallel to $\overrightarrow{\mathbf{b}}\$and $\overrightarrow{\mathbf{c}}\$is anti-parallel to $\overrightarrow{\mathbf{b}}$
$\Longrightarrow \ \overrightarrow{\mathbf{a}}\$and $\overrightarrow{\mathbf{c}}$ are anti-parallel
$\Longrightarrow \$Angle between $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{c}}$ is $\pi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.