Question

Using vectors, find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).

Answer 1

Given, \(A \equiv (1, 1, 2); B \equiv (2, 3, 5); C \equiv (1,5,5)\)

\(\therefore\) \(\vec{AB}=(2-1)\hat{i}+(3-1)\hat{j}+(5-2)\hat{k}\)

\(\therefore\) The area of required triangle \(=\frac{1}{2}\bigg|\vec{AB} \times \vec{AC} \bigg|\)

\(\therefore\) Required area \(=\frac{1}{2}\sqrt{61}=\frac{\sqrt{61}}{2}\) sq units.