If the points (-1, 3, 2),(-4, 2, -2),and (5, | vedclass

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(D) Let the points be $A(-1, 3, 2)$,$B(-4, 2, -2)$,and $C(5, 5, \lambda)$.Since the points are collinear,the direction ratios of line segment $AB$ mus

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$10$

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(D) Let the points be $A(-1, 3, 2)$,$B(-4, 2, -2)$,and $C(5, 5, \lambda)$.Since the points are collinear,the direction ratios of line segment $AB$ must be proportional to the direction ratios of line segment $BC$.The direction ratios of $AB$ are $(-4 - (-1), 2 - 3, -2 - 2) = (-3, -1, -4)$.The direction ratios of $BC$ are $(5 - (-4), 5 - 2, \lambda - (-2)) = (9, 3, \lambda + 2)$.For collinearity,the ratio of corresponding direction ratios must be equal:$\frac{-3}{9} = \frac{-1}{3} = \frac{-4}{\lambda + 2}$.From $\frac{-1}{3} = \frac{-4}{\lambda + 2}$,we get:$-1(\lambda + 2) = -4 	imes 3$$-\lambda - 2 = -12$$-\lambda = -10$$\lambda = 10$.

If the points $(-1, 3, 2)$,$(-4, 2, -2)$,and $(5, 5, \lambda)$ are collinear,then $\lambda = $

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