Equation of the plane which passes through the point of intersection of lines x-13=y-21=z-…

Question

Equation of the plane which passes through the point of intersection of lines $\dfrac{x-1}3=\dfrac{y-2}1=\dfrac{z-3}2$ and $\dfrac{x-3}1=\dfrac{y-1}2=\dfrac{z-2}3$ and has the largest distance from the origin is:

Accepted Answer

Point on line 1: $(3t+1,t+2,2t+3)$; point on line 2: $(s+3,2s+1,3s+2)$. Equating gives $t=1,\ s=1$, and the common point is $(4,3,5)$.
The plane through a given point with the largest distance from the origin has normal along the position vector of that point:
$4x+3y+5z=16+9+25=50.$

Solutions · 1