Find the Value of C in a Plane with Points (2,1,3) and (2,1,5) | Plane Equation

[FrostScYthe]

The general equation for a plane is ax + by + cz = k, where a, b, c, k are constants, and the plane is satisfied by points (x,y,z). If a specific plane contains both points (2, 1, 3) and (2, 1, 5), what is the value of c?

The answer is supposed to be c = 0, but I don't know how to get there.

I tried this [(2, 1, 3)-(2, 1, 5)]t + (2, 1, 5) so I get

x = 2
y = 1
z = 5 - 2t

but I don't know what to do from there

 

[LeonhardEuler]

I tried this [(2, 1, 3)-(2, 1, 5)]t + (2, 1, 5) so I get

x = 2
y = 1
z = 5 - 2t

This is the parametric equation for a line, you want to describe a plane. Two points do not give a full description of a plane, so given two arbitrary points you would generally not be able to find 'c' in the equation. But in this particular case, you will see that if you plug in those two points to the original the equation things will cancel out and you'll be able to find 'c'.

 

[MathematicalPhysicist]

it's a system of linear equations:
you have:
2a+b+3c=k
2a+b+5c=k
solve it and get your answer.