Question

Using section formula prove that the points (2,3,4) ,(-1,2,-3) and (-4,1,-10) are collinear.

Answer 1

Answer:

The given points are A(2,−3,4),B(−1,2,1) and C(0, 3,1,2)

Let P be a point that divides AB in the ratio k:1.

Using section formula, the coordinates of P are given by,

( k+1k(−1)+k+1k(2)−3k+1k(1)+4 )

Now, we will find the value of k at which point P coincides with point C.

⇒ k+1−k+2

=0, we get k=2

For k=2, the coordinates of point P are (0, 1/3,2),

i.e., C(0,1/3 ,2) is a point that divides AB externally in the ratio 2:1 and is the same as point P

Hence, points A,B and C are collinear