Question

Using section formula show that the points A(-4,6,10)B(2,4,6)C(14,0,-2)are collinear

Answer 1

yes these are collinear

Answer 2

ANSWER

let point B(2,4,6) divides the join of A(-4,6,10) C(14,0,-2) in the ratio k:1

 (i...e) the co-ordinates of point B are

 [14 k-4/k+1,0 k+6/k+1, -2 k +10/k+1]

  On putting 14 k-4/k+1 =2

               14 k-4 =2 k+2

                2 k+2

                   12 k=6

                    k=1/2

when

k=1/2, 0 k+6/k+1= 0[1/2]+6/1/2+1=4 and -2 k+10/k+1=-2[1/2]+10/1/2+1=6

 (i....e)point B(2,4,6) divides the join of A(-4,6,10)C(14,0,-2) IN THE RATIO 1/2:1 (or )1:2 internally.

hens A,B,C are collinear and ratio of division at B is 1:2.