Determine scalar, vector and parametric equations for the plane that passes through the points A(1,-2,0), B(1,-2,2), and C(0,3,2).
This is what I got...
AB
AB=OA-OB
=(1,-2,2)-(1,-2,0)
=(0,0,2)
AC=OA-OC
=(0,3,2)-(1,-2,0)
=(-1,5,2)
AB x AC
(0)(2)-(5)(2)
=0-10
=-10
(2)(-1)-(2)(0)
=-2-0
=-2
(0)(5)-(-1)(0)
=0
The normal vector is (-10,-2,0).
-10x-2y+0z+d=0
-10(1)-2(-2)+0(0)+d=0
-10+4+d=0
-6+d=0
d=6
The scalar equation is -10x-2y+6=0
The vector equation is (1,-2,0) + s(0,0,2) + t(-1,5,2)
Parametric Equations:
x=1-t
y=-2+5t
z=2s+2t
Did I do this right?
Thanks for the help in advance.
