Problem:Find the equation of the plane that passes through the line of intersection of the planes, x + y - z = 2 and 2x - y + 3z = 1 and passes throught the point (-1,2,1). |
> Plane1 := x + y -z = 2; Plane2 := 2*x - y + 3*z = 1;
Plane1 := x + y - z = 2 Plane2 := 2 x - y + 3 z = 1
Line := {y = 5/3 z + 1, x = - 2/3 z + 1, z = z} Point := [ -1, 2, 1 ]
p1 := {y = 1, x = 1, 0 = 0} p2 := {1 = 1, y = 8/3, x = 1/3}
n := [ 2/3, -4/3, 8/3 ]
ThePlane := 2/3 x + 2/3 - 4/3 y + 8/3 z = 0
2/3 x - 4/3 y + 8/3 z + 2/3 = 0
2 x - 4 y + 8 z + 2 = 0
Pretty simple ha! |