determine whether work is scalar or vector.

right the question im finding tricky is:

by considering a body doing work against gravity, moving up a hill, determine whether work done is scalar or vector?
(2 mark question)

so i've draw like a triangle an arrow for force at an angle theta form the horizontal which has an arrow along for displacement d.
so i do d.F.cos theta = work.
but how does that justify that work is a scalar? im completly lost.
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 Recognitions: Homework Help The definition of work done by a force $$\vec{F}$$ from points 1 to 2 is $$\int_{1}^2\vec{F}\cdot d\vec{r}$$, which shows that work is a scalar. (The scalar product of two vectors is a scalar.)
 should i just say... since f and r are along same plane theta between the 2 vectors = 0 so using equation: A.B = mod (A).mod(B) cos theta cos theta = 1 (because theta = 0) so u get F.r = mod(F).mod(r) = work so work is the product of the magnitudes of both F an r which gives a scalar product? I draw a hill facing other direction to show that work is independant of direction?

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