Question

Find the volume of the parallelepiped whose coterminous edges are represented by the vector $a=2i-3j+4k$, vector $b=i+2j-k$, vector $c=3i-j+2k$.

• A. $7$
• B. $8$
• C. $9$
• D. none of these

Answer 1

The correct option is A

$7$

Find the volume of the parallelepiped

Given vectors, $a=2i-3j+4k$, $b=i+2j-k$ and $c=3i-j+2k$

We know that, volume $=\left|\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]\right|$

So,

$=\left|\begin{array}{ccc}2& -3& 4\\ 1& 2& -1\\ 3& -1& 2\end{array}\right|$

$$\begin{gathered} =\left|2(4-1)+3(2+3)+4(-1-6)\right| \\ =\left|6+15-28\right| \\ =\left|-7\right| \end{gathered}$$

$=7$

Hence, option $A$ is the correct answer.