Projection of a Vector onto a Plane
Recall that the vector projection of a vector u ⇀ onto another vector v ⇀ is given by projv ⇀u ⇀ = u ⇀·v ⇀v ⇀2v ⇀.
The projection of u ⇀ onto a plane can be calculated by subtracting the component of u ⇀ that is orthogonal to the plane from u ⇀. If you think of the plane as being horizontal, this means computing u ⇀ minus the vertical component of u ⇀, leaving the horizontal component. This "vertical" component is calculated as the projection of u ⇀ onto the plane normal vector n ⇀.
projPlaneu ⇀ = u ⇀ − projn ⇀u ⇀ = u ⇀ − u ⇀·n ⇀n ⇀2n⇀
Choose the coordinates of a plane normal vector n⇀ and a vector u ⇀ and notice how the perpendicular of the vector projection of u ⇀ onto n⇀ is the projection of u ⇀ onto the plane.
Normal Vector n⇀
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