Vector Orientation

Let theta be the angle between two vectors. If 0<theta<pi, the vectors are positively oriented. If pi<theta<2pi, the vectors are negatively oriented.

Two vectors in the plane

 [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 Web Resource.

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