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# If the points $A(-1, 3, 2),\; B(-4, 2, -2)$ and $C (5, 5, \lambda)$ are collinear, find the value of $\lambda$

$(A) \; \lambda=-10$
$(B) \; \lambda = 10$
$(C)\; \lambda = 6$
$(D)\; \lambda = -6$

$\frac{x+1}{-4+1} = \frac{y-3}{2-3} = \frac{z-2}{-2-2}$
$\frac{x+1}{-3} = \frac{y-3}{-1} = \frac{z-2}{-4}$
$\frac{x+1}{3} = \frac{y-3}{1} = \frac{z-2}{4}$
$\frac{5+1}{3}= \frac{5-3}{1} = \frac{\lambda - 2}{4}$
$\implies 2 = 2 = \frac{\lambda - 2 }{4}$
$\implies \lambda = 10$