A school’s media team identifies three points A, B and C on a large bulletin board to position…

A school’s media team identifies three points A, B and C on a large bulletin board to position three charts. The position vectors of A, B and C are $\vec{a} = \hat{i} + 4\hat{j} + 2\hat{k}$, $\vec{b} = 3\hat{i} - 3\hat{j} - 2\hat{k}$ and $\vec{c} = -2\hat{i} + 2\hat{j} + 6\hat{k}$ respectively. They are placed in such a way that a triangle is formed. Find the area of the triangle ABC.