# Thread: Equation to the plane.

1. ## Equation to the plane.

Find an equation of the plane that passes through the points (4, 2, 1) and (-4, 7, 9) and is parallel to the z-axis.

So i know i need a point (x,y,z) and a normal vector n=<a,b,c> i have two points but how do i get a normal vector with the two points given?. I know that the final equation will be in form
ax+by+d=0 with the z axis missing because its parallel to it. Thank you. If possible can you give me the final answer so i can see what im working towards.

2. ## Re: Equation to the plane.

Originally Posted by petenice
Find an equation of the plane that passes through the points (4, 2, 1) and (-4, 7, 9) and is parallel to the z-axis.

So i know i need a point (x,y,z) and a normal vector n=<a,b,c> i have two points but how do i get a normal vector with the two points given?. I know that the final equation will be in form
ax+by+d=0 with the z axis missing because its parallel to it. Thank you. If possible can you give me the final answer so i can see what im working towards.
Yes, the equation is of the form ax+ by+ d= 0. Further, since you can divide that equation by any number without changing the line it represents, you can assume that one of a, b, and d is 1.

Since (4, 2, 1) and (-4, 7, 9) are in the plane that they must satisfy the equation. That gives you two equations to solve for the remaining two values.

3. ## Re: Equation to the plane.

Originally Posted by HallsofIvy
Further, since you can divide that equation by any number without changing the line it represents, you can assume that one of a, b, and d is 1.
Im not clear on what this mean. How does this help me get a normal vector?

4. ## Re: Equation to the plane.

It doesn't it give you the pane, which is what you want!

5. ## Re: Equation to the plane.

Ok got it. 5x+8y-36=0 Thank You