Question

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