Finding out a equation of a plane that is parallel to a plane

[salistoun]

Hi all,

What is the formula of an equation of a plane that is parallel to the plane.

For example the plane is x - 3y -2z -4 = 0 going through a point(1 , 1, 1).

Thanks,
Stephen

 

[HallsofIvy]

The equation of a plane perpendicular to vector <A, B, C>, passing through point $(x_0, y_0, z_0)$ is $A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$ or, equivalently, $Ax+ By+ Cz- (Ax_0+ By_0+ Cz_0)= 0$.

If two planes are parallel they are perpendicular to the same vectors.

Write a vector is x- 3y- 2x- 4= 0 perpendicular to? What is the equation of the plane perpendicular to that vector containing (1, 1, 1)?