Vectors A and B are drawn from a common point. Vector A has magnitude A and angle B A measured in the sense from the + x-axis to the +y-axis. The corresponding quantities for vector B are B and θ B •. Then A = Acos θAi + A sin θ AJ, B = B cos θ B I + B sin θ B.J, and .Φ = |θ B – θA| is the angle between 1 and B.
(a) Derive Eq. (1.18) from Eq. (1.21).
(b) Derive Eq. (1.22) from Eqs. (1.27).