If the x-coordinate of a point P on the line | vedclass

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(B) Let $P$ divide the line segment joining $Q(2,2,1)$ and $R(5,1,-2)$ in the ratio $m:1$. Using the section formula, the coordinates of $P$ are given

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$-1$

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(B) Let $P$ divide the line segment joining $Q(2,2,1)$ and $R(5,1,-2)$ in the ratio $m:1$. Using the section formula, the coordinates of $P$ are given by: $P = \left( \frac{5m+2}{m+1}, \frac{m+2}{m+1}, \frac{-2m+1}{m+1} \right)$. Given that the $x$-coordinate of $P$ is $4$, we have: $\frac{5m+2}{m+1} = 4$. Multiplying both sides by $(m+1)$, we get: $5m + 2 = 4(m + 1) \Rightarrow 5m + 2 = 4m + 4$. Solving for $m$, we get $m = 2$. Now, substitute $m = 2$ into the expression for the $z$-coordinate: $z = \frac{-2(2) + 1}{2 + 1} = \frac{-4 + 1}{3} = \frac{-3}{3} = -1$. Therefore, the $z$-coordinate of $P$ is $-1$.

If the $x$-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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