Q21 of 44 Page 1057

Show that the points having position vectors are collinear, whatever be .

Through the vertices we get the adjacent vectors as,

To prove that A, B, C are collinear we need to prove that

So,

Here,

have

Thus, substituting the values of ,

in equation (i) we get

⇒

Thus, A, B and C are collinear.

19 B

Using vector method, show that the given points A, B, C are collinear:

A(6, −7, −1), B(2, −3, 1) and C(4, −5, 0).

Show that the point A, B, C with position vectors , and respectively are collinear.

Show that the points having position vector , and are collinear, whatever be .

Find a unit vector perpendicular to the plane ABC, where the points A, B, C, are , and respectively.