Find an equation of the plane that passes through the points (0-2,5) and (-1,3,1) and is perpendicular to the plane 2z = 5x + 4y
Here's what I have so far: The plane through (0,-2,5) is ax + b(y+z) + c(z-5) = 0 And the plane also passes through (-1,3,1) so I get: -a + 5b - 4c = 0 (equation 1)
When I looked at the explanation it says:
Now we know that the plane is perpendicular to 5x + 4y - 2z = 0 and then it replaces (x,y,z) with (a,b,c) to get 5a + 4b - 2c = 0 (equation 2)
It continues from there saying to solve the two equations to get (a/6) = (b/-22) = (c/-29)
I know how to solve it once it gets to this but I have absolutely no idea how they got to this step.