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An affine coordinate system has unit vectors that are not mutually orthogonal. The x and y axes in the sketch constitute such a system for a planar situation. A vector may be represented in terms of its contravariant components relative to xy by constructing lines parallel to the respective coordinate axes. Such a set of components are F^{1} and F^{2} for the force vector in the sketch. The unit vectors parallel to the x and y axes are _{1} and _{2}. This force can also be represented in term of its FX and FY components relative to the Cartesian XY coordinate system whose X axis is coincident with x. Given that F_{X} = 500 N, F_{Y} = 350 N, and β = 65°, use vector algebra to determine F^{1} and F^{2}.
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