Question

The area of the parallelogram whose adjacent sides are $\hat{i}-\hat{k}$ and $2\hat{j}+3\hat{k}$ is

• A. $2$
• B. $4$
• C. $\sqrt{17}$
• D. $2\sqrt{13}$

Answer 1

Answer: (C)

$\sqrt{17}$

$\overrightarrow{a}=\hat{i}-\hat{k}$ & $\overrightarrow{b}=2\hat{j}+3\hat{k}=0\hat{i}+2\hat{j}+3\hat{k}$
$\therefore \overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 0& -1\\ 0& 2& 3\end{array}\right|$
$=\hat{i}(0+2)-\hat{j}(3-0)+\hat{k}(2-0)$
$=2\hat{i}-3\hat{j}+2\hat{k}$
$\therefore$ Required area of the parallelogram
$=|\overrightarrow{a}\times \overrightarrow{b}|=|2\hat{i}-3\hat{j}+2\hat{k}|$
$=\sqrt{2^2+3^2+2^2}=\sqrt{17}$