Q19 B of 44 Page 1057

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).


Through the vertices we get the adjacent vectors as,



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


.


So,



Here,


We


have


⇒


Thus, substituting the values of ,


in equation (i) we get


⇒


⇒


Thus, A, B and C are collinear.


More from this chapter

All 44 →
18 D

Using vectors, find the area of ΔABC whose vertices are

A(1, −1, 2), B(2, 1, −1) and C(3, −1, 2).


 19

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

A(3, −5, 1), B(−1, 0, 8) and C(7, −10, −6)


 20

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

 21

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