# Math Help - Plane Equation

1. ## Plane Equation

Write an equation of the plane with normal vector passing through the point in scalar form:
-6x+(-7)y+(-3)z+180

$(-6)x + (-7)y + (-3)z = D$
$(-6)\cdot 2 + (-7)\cdot (-9) + (-3)\cdot (-3) = 60 = D$
3. If $n = \left\langle { - 6, - 7, - 3} \right\rangle$ is the normal the we can use any multiple, so let $n = \left\langle { 6, 7, 3} \right\rangle$.
The general plane is $6x + 7y + 3z + d = 0$.
Now substitute the point to find d: $6(2) + 7( - 9) + 3( - 3) + d = 0 \Rightarrow \quad d = 60$.