Show that the points A, B and C with position vectors, respectively form the vertices of a right angled triangle.

O be the origin,

Let

And

Now we find the vectors

……….(1)

………….(2)

……….(3)

Adding equations (1), (2) and (3)

Therefore, ABC form a triangle.

Now, we want to prove that it is a right angled triangle.

Therefore, the triangle satisfies the Pythagoras theorem. Hence, proved the given vectors form a right angled triangle.

17