Show that the points A, B, C with position vectors 2i - j + k, i - 7j - 9k and 3i - 8j - 8k respectively, are the vertices of a right angled triangle. Hence find the area of the triangle.

Distance between A and B is √(2-1)²+(-1+7)²+(1+9)²=√41
Distance between B and C is √(1-3)²+(-7+8)²+(-9+8)²=√6
Distance between C and A is √(3-2)²+(-8+1)²+(-8-1)²=√35
We can clearly see that BC²+AC²=AB²
By pythogorean theorem ABC form a right angled triangle with right angle at C
Area of triangle=1/2 × BC × AC ⇒1/2 × √6 × √35 ⇒√210/2