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Perp Dot Product


The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector rotated 90 degrees to the left defined by Hill (1994). It satisfies the identities

a^_|_·b=|a||b|sintheta
(1)
(a^_|_·b)^2+(a·b)^2=|a|^2|b|^2
(2)

where theta is the angle from vector a to vector b.


See also

Dot Product, Perpendicular Vector, Vector Multiplication

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References

Hill, F. S. Jr. "The Pleasures of 'Perp Dot' Products." Ch. II.5 in Graphics Gems IV (Ed. P. S. Heckbert). San Diego: Academic Press, pp. 138-148, 1994.

Referenced on Wolfram|Alpha

Perp Dot Product

Cite this as:

Weisstein, Eric W. "Perp Dot Product." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerpDotProduct.html

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