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

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(B) Let the point $P$ divide the line segment $QR$ in the ratio $\lambda : 1$.The coordinates of $P$ are given by the section formula as $\left( \frac

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$-1$

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(B) Let the point $P$ divide the line segment $QR$ in the ratio $\lambda : 1$.The coordinates of $P$ are given by the section formula as $\left( \frac{5\lambda + 2}{\lambda + 1}, \frac{2\lambda + 2}{\lambda + 1}, \frac{-2\lambda + 1}{\lambda + 1} \right)$.Given that the $x$-coordinate of $P$ is $4$,we have:$\frac{5\lambda + 2}{\lambda + 1} = 4$Solving for $\lambda$:$5\lambda + 2 = 4(\lambda + 1)$$5\lambda + 2 = 4\lambda + 4$$\lambda = 2$Now,substitute $\lambda = 2$ into the expression for the $z$-coordinate of $P$:$z = \frac{-2\lambda + 1}{\lambda + 1} = \frac{-2(2) + 1}{2 + 1} = \frac{-4 + 1}{3} = \frac{-3}{3} = -1$.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 $R(5, 2, -2)$ is $4$,then the $z$-coordinate of $P$ is:

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