# Vector equation of a line normal to a plane.

• Sep 3rd 2012, 05:24 AM
tammmyl
Vector equation of a line normal to a plane.
Can someone please help me find the vector equation for the line through point R(3,0,-3) normal to the plane
-4x-12y+4z=-24 ?

I have the normal as n = -4i -12j +4k, but am at lost to the next step.

Any help will be greatly appreciated.
• Sep 3rd 2012, 06:09 AM
Plato
Re: Vector equation of a line normal to a plane.
Quote:

Originally Posted by tammmyl
Can someone please help me find the vector equation for the line through point R(3,0,-3) normal to the plane
-4x-12y+4z=-24 ?
I have the normal as n = -4i -12j +4k, but am at lost to the next step.

We can use the normal \$\displaystyle i+3j-k\$ so the the equation of the line is \$\displaystyle <3,0,-3>+t<1,3,-1>\$.
Recall that a line is perpendicular to a plane if it is parallel to the normal of the plane.
• Sep 3rd 2012, 06:14 AM
HallsofIvy
Re: Vector equation of a line normal to a plane.
The obvious point (which I just have to mention) is that when t= 0, this is (3, 0, -3), the given point, and its direction is given by the "slope", <1, 3, -1>, as given by the normal to the plane.