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Q.
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
Vector Algebra
Solution:
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 $\frac{-2\lambda+1}{\lambda+1}=\frac{-4+1}{2+1}=-1$