Question

The three concurrent edges of a parallelepiped represents the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ such that $[\overrightarrow{a}\,\overrightarrow{b}\,\overrightarrow{c}]= \lambda$. Then the volume of the parallelopiped whose three concurrent edges are the three concurrent diagonals of three faces of the given parallelopiped is

• A. $2\lambda$
• B. $3\lambda$
• C. $\lambda$
• D. none of these.

Answer 1

Answer: (A)

$2\lambda$

Answer 2

The reqd. volume of the parallelopiped $=\left[\vec{b}+\vec{c}\,\vec{c}+\vec{a}\,\vec{a}+\vec{b}\right]$ $=2\left[\vec{a}\,\vec{b}\,\vec{c}\right]=2\lambda$.