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Vector Orientation

Vector orientation is defined for an ordered pair of vectors in an oriented plane. For two nonzero vectors, let theta in [0,2pi) be the directed angle measured in the positive rotation sense from the first vector to the second. If 0<theta<pi, the pair is positively oriented. If pi<theta<2pi, the pair is negatively oriented.

Two vectors with coordinates in a positively oriented basis

[x_1; x_2]and [y_1; y_2]

are positively oriented iff the determinant

D=|x_1 y_1; x_2 y_2|>0,

and are negatively oriented iff the determinant D<0.

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Cite this as:

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

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