Question

It is given that work has only magnitude and no direction. But we have different cases in which work done is negative, positive, etc. How is it possible? Isn't the latter statement contradicting with the first one?

Answer 1

Work has only magnitude as it is a scalar quantity because it is a dot product of two vector quantities, namely, force and displacement. W=F.d=Fdcos θ .
Like any scalar quantity work done can both be positive and negative and it doesn't have to be a vector to be so.
If the force and the displacement are parallel and in the same direction (θ = 0), the mechanical work is positive. If the force and the displacement are parallel but in opposite directions (i.e. antiparallel, θ = 180⁰ ), the mechanical work is negative. The positive or negative sign does not says that work is a vector quantity.