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 $Q$ are $(2, 2, 1)$ and $R$ are $(5, 2, -2)$.Using t

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$-2(z	ext{-coordinate of } P)$

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(B) Let the point $P$ divide the line segment $QR$ in the ratio $\lambda : 1$. The coordinates of $Q$ are $(2, 2, 1)$ and $R$ are $(5, 2, -2)$.Using the section formula,the $x$-coordinate of $P$ is given by $x = \frac{5\lambda + 2}{\lambda + 1}$.Given $x = 4$,we have $4 = \frac{5\lambda + 2}{\lambda + 1} \Rightarrow 4\lambda + 4 = 5\lambda + 2 \Rightarrow \lambda = 2$.Now,find the $y$-coordinate of $P$: $y = \frac{2\lambda + 2}{\lambda + 1} = \frac{2(2) + 2}{2 + 1} = \frac{6}{3} = 2$.Next,find the $z$-coordinate of $P$: $z = \frac{-2\lambda + 1}{\lambda + 1} = \frac{-2(2) + 1}{2 + 1} = \frac{-3}{3} = -1$.Comparing the coordinates,we see that $y = 2$ and $z = -1$. Thus,$y = -2(z)$.Therefore,the $y$-coordinate of $P$ is $-2(z	ext{-coordinate of } P)$.

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 $y$-coordinate of $P$ is:

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