Question

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

Answer 1

$A(5,5,\lambda ),B(-1,3,2)$ and C $(-4,2,-2)$ are collinear.

find value $\lambda$

$\to$ equation for line passing from two point B & C

$\therefore \frac{x+1}{-4+1}=\frac{y-3}{2-3}=\frac{z-2}{-2-2}$

$\therefore \frac{x+1}{-3}=\frac{y-3}{-1}=\frac{z-2}{-4}$

$\therefore \frac{x+1}{3}=\frac{y-3}{1}=\frac{z-2}{4}$

$\to$ point A,B & C is collinear,

So, $\frac{5+1}{3}=\frac{5-3}{1}=\frac{\lambda -2}{4}$

$\therefore 2=2=\frac{\lambda -2}{4}$

$\therefore \lambda -2=8$

$\therefore \lambda =8+2$

$\therefore \lambda =10$