Vector projection

Uncommon card · No. 159052

The vector projection, also known as the vector component or vector resolution, of a vector a on (or onto) a non-zero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b ⁡ a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a∥b. The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted oproj b ⁡ a {\displaystyle \operatorname {oproj} _{\mathbf {b} }\mathbf {a} } or a⊥b), is the orthogonal projection of a onto the plane (or, in general, hyperplane) that is orthogonal to b. Since both...

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