Question

If $x$ coordinate of a point P of line joining the points $Q(2,2,1)$ and $R(5,2,-2)$ is $4$, then the $z$ coordinate of $P$ is

• A. $-2$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

Answer: (B)

Suppose $P$ divides $QR$ in the ratio $\lambda :1$, then
coordinates of $P$ are $\left(\frac{5\lambda +2}{\lambda +1},\frac{2\lambda +2}{\lambda +1},\frac{-2\lambda +1}{\lambda +1}\right)$
Since, the $x$ coordinate of $P$ is $4$ i.e., $\frac{5\lambda +2}{\lambda +1}=4$
$\Rightarrow \lambda =2$
So, $z$ coordinate of $P$ is $\frac{-2\lambda +1}{\lambda +1}=\frac{-4+1}{2+1}=-1$