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Vector Projection


The vector projection of a vector a onto a nonzero vector b is

 proj_(b)a=(a·b)/(||b||^2)b.

It is the component of a parallel to b. Its signed coefficient along the unit vector b/||b|| is the scalar projection. The difference a-proj_(b)a is orthogonal to b.


See also

Dot Product, Orthogonal Projection, Projection, Scalar Projection

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References

Marsden, J. E. and Tromba, A. J. Vector Calculus, 5th ed. New York: W. H. Freeman, 2003.

Cite this as:

Weisstein, Eric W. "Vector Projection." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VectorProjection.html

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