Question

If the points A(2, 1, 1), B(0, -1, 4) and C(k, 3, -2) are collinear, then k 

(A) 0

(B) 1

(C) 4

(D) -4

Answer 1

(c) 4 
solution:
Direction Ratio of bar(AB )=(-2, -2, 3)
Direction Ratio of bar(BC)=(k, 4, -6)

If point A,B and C are collinear then `("DR of "bar(AB))/("DR of "bar(BC))`=constatnt

`-2/k=-2/4`

`k=4`