Question

If the volume of the parallelopiped with $\vec{a},\vec{b}$ and $\vec{c}$ as coterminous edges is $40cubic$ units, then the volume of the parallelopiped having $\vec{b}+\vec{c},\vec{c}+\vec{a}$ and $\vec{a}+\vec{b}$ as coterminous edges in cubic units is

• A. 40
• B. 80
• C. 120
• D. 160

Answer 1

Answer: (B)

Given, volume of parallelopiped
$[\vec{a}\vec{b}\vec{c}]=40$
$\therefore$ Volume of parallelopiped
$\vec{b}+\vec{c}\vec{c}+\vec{a}\vec{a}+\vec{b}]$
$=2[\vec{a}\vec{b}c]$
$=2\times 40=80$ cu unit