# Find the Plane: Perpendicular to yz-Plane & y=-2, z=4

• adrimare
In summary, the student is trying to determine the equation of a perpendicular plane that has y-intercept at 4 and z-intercept at -2. The normal to the plane is perpendicular to this vector, so the plane is located at (0,1,1). The student is trying to find the equation of the plane using the y- and z-intercepts at 4 and -2, but is having trouble because the normal is not <0, 1, 1>.

## Homework Statement

Determine the Cartesian equation of the plane that is perpendicular to the yz-plane and has y-intercept 4 and z-intercept -2.

?

## The Attempt at a Solution

I'm pretty sure that the normal to the plane I want to find would be (0,1,1). A y-intercept would go through (0,y,0) and a z-intercept would go through or be (0,0,z). How do I make an equation with a y and z- intercept at 4 and -2 respectively?

adrimare said:

## Homework Statement

Determine the Cartesian equation of the plane that is perpendicular to the yz-plane and has y-intercept 4 and z-intercept -2.

?

## The Attempt at a Solution

I'm pretty sure that the normal to the plane I want to find would be (0,1,1). A y-intercept would go through (0,y,0) and a z-intercept would go through or be (0,0,z). How do I make an equation with a y and z- intercept at 4 and -2 respectively?
No, the normal to the plane is NOT <0, 1, 1>. The normal is perpendicular to this vector. The plane is perpendicular to the y-z plane. The y-intercept is 4, which means that the point (0, 4, 0) is on the plane. The z-intercept is -2, which means that what point is on the plane?

If you're not already doing so, draw a sketch using a three-dimensional coordinate system. It will help you get your head around these kinds of problems.

My teacher said to forget about learning how to sketch, so that's out. Is the normal to the plane (1,0,0) then? So (0,4,0) and (0,0,-2) are both on the plane. How would I stick those points on a plane with a Cartesian equation of x=0, then? I need to get a D-value, which I can get from points, I know, but when the equation is 1x + 0y + 0z + D, would the intercepts kind of not really matter? The D-value would be 0, so the equation would be x=0, right? Or am I wrong about the normal again? Or am I supposed to be looking for the direction vector formed by the two intercepts and use that as my normal?