Question

Forula to find distance betweent point and plane 3d emoetry

Answer 1

Answer:

Here's a quick sketch of how to calculate the distance from a point P=(x1,y1,z1) to a plane determined by normal vector N=(A,B,C) and point Q=(x0,y0,z0). The equation for the plane determined by N and Q is A(x−x0)+B(y−y0)+C(z−z0)=0, which we could write as Ax+By+Cz+D=0, where D=−Ax0−By0−Cz0.

This applet demonstrates the setup of the problem and the method we will use to derive a formula for the distance from the plane to the point P.

Distance from point to plane. A sketch of a way to calculate the distance from point P (in red) to the plane. The vector n (in green) is a unit normal vector to the plane. You can drag point P as well as a second point Q (in yellow) which is confined to be in the plane. Although the vector n does not change (as the plane is fixed), it moves with P to always be at the end of a gray line segment from P that is perpendicular to the plane. This distance from P to the plane is the length of this gray line segment. This distance is the length of the projection of the vector from Q to P (in purple) onto the normal vector n.

✔️Hope it will help you.✔️