Given the equation x + z = 2.
Is P parallel to any of the coordinate planes?
Is P perpendicular to any of the coordinate planes?
P given by the equation x + z = 2
P is parallel to the y-axis, perpendicular to the x-z plane.
The plane x=3 is perpendicular to the x-axis, parallel to y-z plane.
Thanks!
To determine whether a plane is parallel or perpendicular to a coordinate plane, we need to examine the coefficients of the variables in the equation of the plane.
For the equation x + z = 2, we can rearrange it to the form z = -x + 2.
1. To determine if P is parallel to any of the coordinate planes:
- A plane is considered parallel to a coordinate plane if it does not contain any variable(s) corresponding to that plane.
- In this case, we can see that the equation of the plane only contains variables x and z, but not y. Therefore, P is parallel to the yz-plane.
2. To determine if P is perpendicular to any of the coordinate planes:
- A plane is considered perpendicular to a coordinate plane if the coefficient of the variable corresponding to that plane is 0.
- In the given equation, the coefficient of y is 0 (since y is not present in the equation). Therefore, P is perpendicular to the xy-plane.
In summary, for the equation x + z = 2:
- P is parallel to the yz-plane.
- P is perpendicular to the xy-plane.