Question

A parallelopiped has edges described by the $\hat{i}+2\hat{j}$, $4\hat{j}$ and $\hat{j}+3\hat{k}$. Then the volume is:

• A. 11
• B. 12
• C. 15
• D. 28

Answer 1

The correct option is B 12

Let the edges of parallelopiped be $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$.

Volume of a parallelopiped $=|\overrightarrow{a}\cdot (\overrightarrow{b}\times \overrightarrow{c})|$

Here, $\overrightarrow{a}=\hat{i}+2\hat{j}\overrightarrow{b}=4\hat{j}\overrightarrow{c}=\hat{j}+3\hat{k}\Rightarrow \overrightarrow{b}\times \overrightarrow{c}=12\hat{i}$

$\Rightarrow V=(\hat{i}+2\hat{j})\cdot 12\hat{i}\Rightarrow V=12$