Question

If the position vector of the vertices of a triangle are $\hat{i}-\hat{j}+2\hat{k};2\hat{i}+\hat{j}+\hat{k}$ & $3\hat{i}-\hat{j}+2\hat{k}$, then find the area of the triangle.

• A. $\sqrt{5}{m}^2$
• B. $5m^2$
• C. $25m^2$
• D. $2m^2$

Answer 1

The correct option is A $\sqrt{5}{m}^2$

We know that

Area of triangle is half times the cross product of two adjacent vector given by

Area of triangle $=\frac{1}{2}\left|\begin{array}{c}\overrightarrow{A}\times \overrightarrow{B}\end{array}\right|=\frac{1}{2}\left(\begin{array}{c}4\hat{k}+2\hat{j}\end{array}\right)$

$\overrightarrow{Area}=\left(\begin{array}{c}\hat{j}+2\hat{k}\end{array}\right)$

$\left|\begin{array}{c}Area\end{array}\right|=\sqrt{5}{m}^2$