If we apply a second affine transformation ( {b} = (r(ϕ), ∼ {b}) ) to ( ∼ {w} ), what is the resulting 2-component vector ( ∼ {u} ) in terms of ( r(θ) ), ( r(ϕ) ), ( ∼ {a} ), ( ∼ {b} ), and ( ∼ {v} )?
a) ( ∼ {u} = r(θ) ⋅ r(ϕ) ⋅ ∼ {a} + ∼ {b} + ∼ {v} )
b) ( ∼ {u} = r(θ) + r(ϕ) + ∼ {a} ⋅ ∼ {b} + ∼ {v} )
c) ( ∼ {u} = r(θ) ⋅ ∼ {a} + r(ϕ) ⋅ ∼ {b} + ∼ {v} )
d) ( ∼ {u} = r(θ) ⋅ ∼ {a} + r(ϕ) ⋅ ∼ {b} - ∼ {v} )