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

Suppose P divides QR in the ratio $\mathrm{\lambda }$ : 1. Then, coordinate of P are $\left(\frac{5\mathrm{\lambda }+2}{\mathrm{\lambda }+1},\frac{2\mathrm{\lambda }+2}{\mathrm{\lambda }+1},\frac{-2\mathrm{\lambda }+1}{\mathrm{\lambda }+1}\right)$

Since, the Z-coordinate of P is 4. 

$\begin{array}{l}\frac{5\mathrm{\lambda }+2}{\mathrm{\lambda }+1}=4\\ \Rightarrow \mathrm{\lambda }=2\end{array}$

so, z-coordinate of P is $\frac{-2\mathrm{\lambda }+1}{\mathrm{\lambda }+1}=\frac{-4+1}{2+1}=-1$