 Projection of a Vector onto a Plane - Maple Programming Help

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Projection of a Vector onto a Plane

 Main Concept Recall that the vector projection of a vector  onto another vector  is given by .   The projection of  onto a plane can be calculated by subtracting the component of   that is orthogonal to the plane from  .  If you think of the plane as being horizontal, this means computing   minus the vertical component of , leaving the horizontal component. This "vertical" component is calculated as the projection of   onto the plane normal vector .

Choose the coordinates of a plane normal vector $\stackrel{\mathit{⇀}}{n}$ and a vector  and notice how the perpendicular of the vector projection of  onto $\stackrel{\mathit{⇀}}{n}$ is the projection of  onto the plane.

 Normal Vector $\stackrel{{\mathbf{⇀}}}{{\mathbit{n}}}$ Vector $\stackrel{{\mathbf{⇀}}}{{\mathbit{u}}}$ ${x}_{u}=$ ${y}_{n}=$ ${y}_{u}=$ ${z}_{n}=$ ${z}_{u}=$   More MathApps