Q. If the volume of the parallelopiped with $\overrightarrow{\mathbf{a}},\ \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ as coterminous edges is 40 cu units, then the volume of the parallelopiped having $\overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}},\ \overrightarrow{\mathbf{c}} + \overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}}$ as coterminous edges inn cubic units is
A) 80
B) 120
C) 160
D) 40
Explanation
(a)
Given volume of parallelopiped
$\left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}} \right\rbrack = 40$
$\therefore$ Volume of parallelopiped
$= \left\lbrack \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}}\ \overrightarrow{\mathbf{c}} + \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right\rbrack = 2\left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}} \right\rbrack$
$= 2 \times 40 = 80\ cu\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.