Question

The area of the triangle formed by the adjacent sides with A = $-3\hat{i}+2\hat{j}-4\hat{k}$ and B = $-\hat{i}+2\hat{j}+\hat{k}$ is:

• A. $\frac{\sqrt{165}}{2}$ units
• B. $\frac{\sqrt{137}}{2}$ units
• C. $\sqrt{165}$ units
• D. $\sqrt{137}$ units

Answer 1

The correct option is A $\frac{\sqrt{165}}{2}$ units

Given,

$\overrightarrow{A}=-3\hat{i}+2\hat{j}-4\hat{k}$

$\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k}$

Area of the triangle, $\Delta =\frac{1}{2}|\overrightarrow{A}\times \overrightarrow{B}|$

$\Delta =\frac{1}{2}|(-3\hat{i}+2\hat{j}-4\hat{k})\times (-\hat{i}+2\hat{j}+\hat{k})|$

$\Delta =\frac{1}{2}|10\hat{i}+7\hat{j}-4\hat{k}|$

$\Delta =\frac{\sqrt{(10{)}^2+(7{)}^2+(-4{)}^2}}{2}$

$\Delta =\frac{\sqrt{165}}{2}units$

The correct option is A.