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The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero 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 .
Also, let Q = (x 1, y 1) be any point on this line and n the vector (a, b) starting at point Q. The vector n is perpendicular to the line, and the distance d from point P to the line is equal to the length of the orthogonal projection of on n. The length of this projection is given by:
A square matrix is called a projection matrix if it is equal to its square, i.e. if =. [2]: p. 38 A square matrix is called an orthogonal projection matrix if = = for a real matrix, and respectively = = for a complex matrix, where denotes the transpose of and denotes the adjoint or Hermitian transpose of .
where the operator denotes a dot product, ^ is the unit vector in the direction of , ‖ ‖ is the length of , and is the angle between and . [ 1 ] The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates , the components of a vector are the scalar projections in the directions of the coordinate axes .
To do this, one should pick n as a multiple of 213, because then 113n / 213 is an integer; one then drops n needles, and hopes for exactly x = 113n / 213 successes. If one drops 213 needles and happens to get 113 successes, then one can triumphantly report an estimate of π accurate to six decimal places. If not, one can just do ...
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The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints. The length of a line segment parallel to the projection plane remains unchanged. The length of any line segment is shortened if the projection is an orthographic one. [clarification needed]
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