Question

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

• A. $2$
• B. $7$
• C. $10$
• D. $0$

Answer 1

Answer: (C)

$10$

The equations of the line passing through A(-1,3,2) and B(-4,2,-2) are :

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

or, $\frac{x+1}{3}=\frac{y-3}{1}=\frac{z-2}{4}$ .....(1)

If the points $A(-1,3,2),B(-4,2,-2)$ and $C(5,5,$$\lambda$$)$ are collinear, then the coordinates of C must satisfy equation 1.

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

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

$\lambda =10$