Intersection line of two planes

[debwaldy]

Hello,so this is prob a v v basic question but I am 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

 

[radou]

Hello,so this is prob a v v basic question but I am 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]

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.