Question

The values of a for which $(8,-7,a),(5,2,4)$ and $(6,-1,2)$ are collinear, is given by?

• A. $2$
• B. $-2$
• C. $-1$
• D. $1$

Answer 1

Answer: (A)

$2$

$\begin{array}{c}thena=?\\ TheequationlineABis\\ \Rightarrow \frac{x-8}{5-8}=\frac{y+7}{2+7}=\frac{z-a}{4-a}....\left(1\right)\\ pointcliesinthelineAB\\ point\left(6,-1,2\right)satisfyeq\left(1\right)\\ \Rightarrow \frac{-2}{-3}=\frac{-1+7}{9}=\frac{2-a}{4-a}\\ \Rightarrow \frac{2}{3}=\frac{2-a}{4-a}\\ \Rightarrow 8-2a=6-3a\\ \Rightarrow 3a-2a=6-8\\ a=-2\end{array}$