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)

80

Answer 2

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