Browse Questions

# Find the foot of perpendicular from the point(2,3,-8)to the line $\Large \frac{4-x}{2}\;=\frac{y}{6}\;=\frac{1-z}{3}$.Also,find the perpendicular distance from the given point to the line.

Toolbox:
• If two lines are $\perp$ then $a_1a_2+b_1b_2+c_1c_2=0$, where $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$ are the direction ratios of the two lines.
Step 1:
Let the given equation be $\large\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}=\lambda$.
This can be written as