Unformatted text preview: + −→ k (Figure 4.2 ). It is x y z −→ n −→ x P ( −→ x ) Figure 4.2: Projection onto a Plane geometrically clear that this takes triangles through the origin to triangles through the origin, and hence is linear. Since any vector is the sum of its projection on the plane and its projection on the normal line, we know that P can be calculated from the formula P ( −→ x ) = −→ x − proj −→ u −→ x = −→ x − ( −→ x · −→ u ) −→ u , where −→ u = −→ n / √ 3 is the unit vector in the direction of...
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 Spring '08
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 Calculus, Linear Algebra, Geometry, Vectors, Linear Mappings, scalars α

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