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Work is scalar
Work W is both a scalar (F.D) and a vector (FxD), in short work is a Quaternion,
W = [0,F][0,D]= [00 -F.D, 0D + F0 + FxD] = [-F.D, FxD] .
Physics has yet to recognize that Work and Energy are Quaternions and thus define work and energy as a scalar. Nature and mathematics recognize work as as a Quaternion manifested by the reality of F.D and FxD.
Work is a scalar when the angle between F and D is a multiple of even 90 degrees and a torque when the angle is an odd multiple of 90 degrees.
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RossWork is both! The product of vector force F and vector displacement D gives two terms:
Work W= [0,F][0,D] = [0 - f.D, 0 + 0 + FxD] = [-F.D, FxD] .
Scalar work Ws= [- F.D,0]= -FDcos(FD)
and Vector Work Wv =[0, FxD]= FDsin(FD)v
When F and D are parallel work is a scalar, when F and D are perpendicular, work is a vector, otherwise, work is both a scalar and a vector.
Work like many quantities in Physics is a combination of a scalar and 3 vectors, in short a Quaternion quantity.
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