Show that the points A, B, C with position vectors 2i - j + k, i - 3j - 5k

Question

Show that the points A, B, C with position vectors \(2\hat{i}-\hat{j}+\hat{k},\) \(\hat{i}-3\hat{j}-5\hat{k}\) \(3\hat{i}-4\hat{j}-4\hat{k}\) respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.

Answer 1

Given, Position vector of \(A = 2\hat{i}-\hat{j}+\hat{k}\)

Position vector of \(B = \hat{i}-3\hat{j}-5\hat{k}\)

Position vector of \(C = 3\hat{i}-4\hat{j}-4\hat{k}\)

\(\Rightarrow\) A, B, C are the vertices of right triangle.

Alternate method to find area: