Question

Find a formula for the distance from the point​ P(x,y,z) to each of the following planes. a. Find the distance from​ P(x,y,z) to the​ xy-plane. b. Find the distance from​ P(x,y,z) to the​ yz-plane. c. Find the distance from​ P(x,y,z) to the​ xz-plane

Answer 1

Distance to the xy-plane = |z|

Distance to the yz-plane = |x|

Distance to the xz-plane = |y|

Explanation:

The distance from P(x,y,z) to the xy-plane is by definition the magnitude of the vector that goes from the perpendicular projection of P over the xy-plane to the point P, which is exactly the magnitude of the vector (0,0,z) = |z| the absolute value of z

Similarly, the distance from P to the yz-plane is |x| and the distance from P to the xz-plane is |y|

Distance to the xy-plane = |z|

Distance to the yz-plane = |x|

Distance to the xz-plane = |y|