Projection of a Vector onto a Plane - Maple Help

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Projection of a Vector onto a Plane

 

Main Concept

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

Vector u

xn =

xu=

yn=

yu=

zn=

zu=

 

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