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If $x$-coordinate of a point $P$ on the line joining the points $Q(2,2,1)$ and $R(5,1,-2)$ is 4 , then the $z$-coordinate of $P$ is
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The correct answer is:
$-1$
Let $P$ divide $Q(2,2,1)$ and $R(5,1,-2)$ in the ratio of $m: 1$.
$\therefore \quad P\left(\frac{5 m+2}{m+1}, \frac{m+2}{m+1}, \frac{-2 m+1}{m+1}\right)$
But it is given $\frac{5 m+2}{m+1}=4$.
$\begin{aligned} & \Rightarrow \quad 5 m+2=4 m+4 \\ & \Rightarrow \quad m=2 \\ & \therefore \text { Coordinate of } z=\frac{-2 \times 2+1}{2+1}=\frac{-3}{3}=-1\end{aligned}$
$\therefore \quad P\left(\frac{5 m+2}{m+1}, \frac{m+2}{m+1}, \frac{-2 m+1}{m+1}\right)$
But it is given $\frac{5 m+2}{m+1}=4$.
$\begin{aligned} & \Rightarrow \quad 5 m+2=4 m+4 \\ & \Rightarrow \quad m=2 \\ & \therefore \text { Coordinate of } z=\frac{-2 \times 2+1}{2+1}=\frac{-3}{3}=-1\end{aligned}$
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