Intersection line of two planes

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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 :bugeye:
 

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  • #2
radou
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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 :bugeye:
Can a system of two equations involving three unknowns have a unique solution?
 
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HallsofIvy
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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.
 

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