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?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.
Homework Equations
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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?
To find the coordinates of a plane perpendicular to the yz-plane, you need to set the x-value to a constant value, let's say x=k. This means that the plane will pass through all points with the x-coordinate equal to k. The equation of the plane will then be x=k.
The equation of a plane perpendicular to the yz-plane can be written as x=k, where k is a constant value. Since the plane is perpendicular to the yz-plane, the x-value does not depend on the y and z values. Therefore, the equation would be x=k, where k is any real number. This means that the plane is a vertical plane passing through all points with the x-coordinate equal to k.
To graph a plane perpendicular to the yz-plane with the equation x=3, you need to draw a vertical line at x=3. This line will represent all points on the plane with the x-coordinate equal to 3. Since the plane is perpendicular to the yz-plane, it will also extend infinitely in the y and z directions.
There are infinitely many planes that can be perpendicular to the yz-plane. This is because for any value of x, there is a unique plane that can be perpendicular to the yz-plane. Therefore, there is no limit to the number of planes that can be perpendicular to the yz-plane.
A plane perpendicular to the yz-plane is parallel to the x-axis. This is because the x-axis is defined as the line with a constant x-value of 0, and any plane perpendicular to the yz-plane has a constant x-value. Therefore, the plane and the x-axis never intersect and are always parallel to each other.