# Intersection line of two planes

Hello,so this is prob a v v basic question but im confused as to how one find the equation of the line of intersection of two planes:e.g. 2x + 3y + 5z = 2 & 4x + 2y + z = 11. is there just one unique solution or will the solution involve parameters??eeks ## Answers and Replies

radou
Homework Helper
Hello,so this is prob a v v basic question but im confused as to how one find the equation of the line of intersection of two planes:e.g. 2x + 3y + 5z = 2 & 4x + 2y + z = 11. is there just one unique solution or will the solution involve parameters??eeks Can a system of two equations involving three unknowns have a unique solution?

HallsofIvy
Science Advisor
Homework Helper
is there just one unique solution or will the solution involve parameters??
The question asks for the line at which the two planes intersect. Yes there is a unique line of intersection and, yes, the equation of a line in 3 dimensions involves a parameter!

In general, you can solve two equations for two unknowns. Here, you can solve for two of the unknowns (say, x and y) in terms of the third (z). Then you can use that third unknown as the parameter.