If the x-coordinate of a point P on the join of $Q (2, 2, 1)$and $R (5, 1, -2)$ is 4, then its z-coordinate, is

 

$$\begin{gathered} Given points Q=(2,2,1),R=(5,1,-2) \\ Equation of line through P and Q is \frac{x-2}{5-2}=\frac{y-2}{1-2}=\frac{z-1}{-2-1}=r \\ \Rightarrow \frac{x-2}{3}=r\Rightarrow x=3r+2 \\ \Rightarrow 4=3r+2\Rightarrow 3r=2\Rightarrow r=\frac{2}{3} \\ Now \frac{z-1}{-2-1}=r\Rightarrow \frac{z-1}{-2-1}=\frac{2}{3} \\ \Rightarrow 3z-3=-6 \\ \Rightarrow z=-1 \end{gathered}$$