Question

The points $(5,2,4),(6,-1,2)$ and $(8,-7,k)$ are collinear if $k$ is equal to

• A. -2
• B. 2
• C. 3
• D. - 1.

Answer 1

Answer: (A)

Let $A(5,2,4),B(6,-1,2),C(8,-7,k)$ be the given points.
Direction Ratios of $AB$ are $<6-5,-1-2,2-4>i.e.,<1,-3,-2>$
Direction Ration of BC are $<8,-6,-7,+1k-2>$
i.e., $<2,-6,k-2>$
Since $A,B,C$ are Collinear $\therefore$ $\frac{2}{1}=\frac{-6}{-3}=\frac{k-2}{-2}$
$\therefore$ $k-2=-4\Rightarrow k=2-4=-2$.