Question

if the points A(2, 1, 1), B(0 ,-1 ,4)& C(k ,3 ,-2) are colinear, then k=

Answer 1

determinant of these points are equal to zero .

det{( 2, 1 , 1 ), (0, -1 , 4), (k , 3 ,-2)} =0


2(8-12) -1(0-4k)+1(0+4k)=0

-8 +4k + 4k =0

8k-8 =0

k=1 (answer)

Answer 2

A, B and C are colinear

Determinants of points A,B and C = 0.

det( 2, 1 , 1 ), (0, -1 , 4), (k , 3 ,-2) =0
2(8-12) -1(0-4k)+1(0+4k)=0
16 - 24 + 4k + 4k = 0
8k - 8 = 0
8k = 8
k = 1

Hope This Helps You!