Question

Find the area of triangle whose vectors are (1,1,1), (2,1,3)and (0,0,1) using vectors .

Answer 1

$\overline{OA}=(1,1,1)\overline{OB}=(2,1,3)\overline{OC}=(0,0,1)\overline{AB}=(1,0,2)\overline{AC}=(-1,-1,0)$

$\overline{AB}\times \overline{AC}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 0& 2\\ -1& -1& 0\end{array}\right|=2\overline{i}-2\overline{j}-\overline{k}$

$Area=\frac{1}{2}|\overline{AB}\times \overline{AC}|=\frac{3}{2}squareunits$