Question

Show that the points A, B and C having position vectors (3i - 4j - 4k),(2i - j + k) and (i - 3j - 5k) respectively, form the vertices of a right-angled triangle.

Answer 1

 A =  \(\vec{i}+2\vec{j}+7\vec{k}\)

B =  \(2\vec{i}+6\vec{j}+2\vec{k}\)

 C =  \(3\vec{i}+10\vec{j}-3\vec{k}\)

= -2 -3 + 5

= 0

The triangle is right-angled.