Question

Find the equation of a line passing through the points $P(-1,3,2)$ and $Q(-4,2,-2)$. Also, if the point $R(5,5,\lambda )$ is collinear with the points $P$ and $Q$, then find the value of $\lambda$

Answer 1

Equation of the line passing through the points $P(-1,3,2)$ and $Q(-4,2,-2)$ is
$\frac{x+1}{-1+4}=\frac{y-3}{3-2}=\frac{z-2}{2+2}$
$\frac{x+1}{3}=\frac{y-3}{1}=\frac{z-2}{4}$
$\because$ Point $R(5,5,\lambda )$ lies on it,
$\frac{5+1}{3}=\frac{5-3}{1}$ $=\frac{\lambda -2}{4}\Rightarrow \lambda =10$