What is the distance from the origin to the plane?

Equation in Vector Form \vec{N} = \vec{D} , where \vec{N} is the normal to the plane. If we consider O to be the origin, then the distance of the first plane from the origin is given by ON. Similarly, the distance of the second plane from the origin is given by ON’.

How do you find the distance from the origin?

Distance of a point P(x, y) from the origin is given by d(0,P) = √ x2 + y2.

How to calculate the distance from the origin to the plane?

Do a drawing and focus on the x − axis: you have to draw a segment of line from the origin to the plane and perpendicular to the plane, so together with the point A := ( 4, 0, 0) you get a straignth angle triangle, with vertices A, ( 0, 0, 0), C, C = the point of intersection of the perpendicular to the plane towards the origin (one of the legs).

Which is the shortest distance from a point to a plane?

The shortest distance from a point to a plane is along a line perpendicular to the plane. Therefore, the distance from point P to the plane is along a line parallel to the normal vector, which is shown as a gray line segment. If we denote by R the point where the gray line segment touches the plane, then R is the point on the plane closest to P.

Which is a normal vector 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.

Is there a way to drag point P 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.