Question

Given two planes: x+y+z=1, and x-2y+3z=1. Find the symmetric equations for the line of intersection L of these two planes.

Answer 1

first, find the vector parallel to the line of intersection by taking <1, 1, 1> cross <1, -2, 3>

Answer 2

right, i did that. Now, how do i obtain a point i need to write the equations of the line

Answer 3

set z = 0 for each equation then solve

so you need to solve
x + y = 1
x - 2y = 1

Answer 4

subtract those two and you get 3y = 0

so y = 0 and x = 1

Answer 5

point (1,0,0)

Answer 6

yep, your point of instersection would be (1, 0, 0)

Answer 7

okay, thanks