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

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(B) Let point $P$ 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 $P$

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$-1$

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(B) Let point $P$ 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: $\frac{5m + 2}{m + 1} = 4$. Solving for $m$: $5m + 2 = 4(m + 1) \Rightarrow 5m + 2 = 4m + 4 \Rightarrow m = 2$. Now,substitute $m = 2$ into the expression for the $z$-coordinate: $z = \frac{-2m + 1}{m + 1} = \frac{-2(2) + 1}{2 + 1} = \frac{-4 + 1}{3} = \frac{-3}{3} = -1$. Thus,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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