Mathematics - Straight Lines Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{A}(1,-1,2)\\ & \mathrm{B}(5,7,-6)\\ & \mathrm{C}(3,4,-10)\\ & \mathrm{D}(-1,-4,-2)\\ & \text{ Area }=\frac{1}{2}|\overrightarrow{\mathrm{AC}}\times \overrightarrow{\mathrm{BD}}|=\frac{1}{2}|(2\hat{\mathrm{i}}+5\hat{\mathrm{j}}-12\hat{\mathrm{k}})\times (6\hat{\mathrm{i}}+11\hat{\mathrm{j}}-4\hat{\mathrm{k}})|\\ & =\frac{1}{2}|112\hat{\mathrm{i}}-64\hat{\mathrm{j}}-8\hat{\mathrm{k}}|\\ & =4|14\hat{\mathrm{i}}-8\hat{\mathrm{j}}-\hat{\mathrm{k}}|\\ & =4\sqrt{196+64+1}\\ & =4\sqrt{261}\\ & =12\sqrt{29}\end{array}$