If the line passes through the points P(6, -1 | vedclass

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(C) Since the points $P(6, -1, 2)$,$Q(8, -7, 2\lambda)$,and $R(5, 2, 4)$ are collinear,the direction ratios of the line segments $PQ$ and $PR$ must be

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$-1$

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(C) Since the points $P(6, -1, 2)$,$Q(8, -7, 2\lambda)$,and $R(5, 2, 4)$ are collinear,the direction ratios of the line segments $PQ$ and $PR$ must be proportional.The direction ratios of $PQ$ are $(8-6, -7-(-1), 2\lambda-2) = (2, -6, 2\lambda-2)$.The direction ratios of $PR$ are $(5-6, 2-(-1), 4-2) = (-1, 3, 2)$.Since the points are collinear,the ratio of the direction ratios must be equal:$\frac{2}{-1} = \frac{-6}{3} = \frac{2\lambda-2}{2}$$-2 = -2 = \lambda-1$Equating the last part: $-2 = \lambda-1$,which gives $\lambda = -1$.

If the line passes through the points $P(6, -1, 2)$,$Q(8, -7, 2\lambda)$,and $R(5, 2, 4)$,then the value of $\lambda$ is $.......$

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