Let L be the line through (1, 2, 3) and (3, 1, 2) and let L' be the line through (1, −1, 1) and (0, 2, 1). a) find Find the equation of a plane π containing L, and parallel to a plane containing L'. b)Find a point p ∈L and a point p'∈L' such that p − p' is orthogonal to both L and L'
A) so for A what I did was find the equation of both lines (parametric equation) L=(x,y,z) = (1,2,3) +t(2,-1,-1) L'=(x,y,z) = (1,-1,1) + t (-1,3,0)
Next thing I did was find a normal vector for these planes that have to be parallel to eachother, buy doing the crossproduct of the direction vectors of the two lines, and got n=[3,1,5]
Now I have no clue how to write the equation of these two planes, because dont I need a 3rd point to write one an equation of a plane?
b) have no clue where to start
Thank for your help!