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The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted or a ⊥b), [1] is the orthogonal projection of a onto the plane (or, in general, hyperplane) that is orthogonal to b.
A projection on a vector space is a linear ... is an orthogonal projection onto the xy-plane. This function is represented by the matrix ...
Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
The projection of the point C itself is not defined. The projection parallel to a direction D, onto a plane or parallel projection: The image of a point P is the intersection of the plane with the line parallel to D passing through P. See Affine space § Projection for an accurate definition, generalized to any dimension. [citation needed]
In either the coordinate or vector formulations, one may verify that the given point lies on the given plane by plugging the point into the equation of the plane. To see that it is the closest point to the origin on the plane, observe that p {\displaystyle \mathbf {p} } is a scalar multiple of the vector v {\displaystyle \mathbf {v} } defining ...
From January 2008 to March 2011, if you bought shares in companies when Lucille S. Salhany joined the board, and sold them when she left, you would have a -16.7 percent return on your investment, compared to a -11.6 percent return from the S&P 500.
If 0° ≤ θ ≤ 90°, as in this case, the scalar projection of a on b coincides with the length of the vector projection. Vector projection of a on b (a 1), and vector rejection of a from b (a 2). In mathematics, the scalar projection of a vector on (or onto) a vector , also known as the scalar resolute of in the direction of , is given by:
From November 2011 to December 2012, if you bought shares in companies when Gaurdie E. Banister Jr. joined the board, and sold them when he left, you would have a 0.3 percent return on your investment, compared to a 17.3 percent return from the S&P 500.