Question

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

• A. $-10$
• B. 5
• C. $-5$
• D. 10

Answer 1

Answer: (D)

Three points $\left(x_1, y_1, z_1\right),\left(x_2, y_2, z_2\right)$ and $\left(x_3, y_3, z_3\right)$ are collinear if
$ \frac{x_2-x_1}{x_3-x_1}=\frac{y_2-y_1}{y_3-y_2}=\frac{z_2-z_1}{z_3-z_2} $
$\rightarrow \frac{-4-(-1)}{5-(-4)}=\frac{2-3}{5-2}=\frac{-2-2}{\lambda+2}$
$\rightarrow \frac{-3}{9}-\frac{-1}{3}=\frac{-4}{\lambda+2} \rightarrow \frac{-1}{3}=\frac{-4}{\lambda+2}$
$\rightarrow \lambda+2=12$
$\rightarrow \lambda=10$