Answer
(a) $164. 75^{\circ}$
(b) $28.07^{\circ}$
c)$90.0^{\circ}$
Work Step by Step
(a)
cos φ=$ \frac{AxBx+AyBy}{AB}$
=$\frac{(-2.00) (2.00)+(6.00)(-3.00)}{(\sqrt (-2.00)^{2}+\sqrt (6.00)_{y} (\sqrt (2.00)^{2}+\sqrt (-3.00)^{2}}$
=-0.964764 -> φ = $164. 75^{\circ}$
(b)
cos φ=$ \frac{AxBx+AyBy}{AB}$
=$\frac{(3.00) (10.00)+(5.00)(6.00)}{(\sqrt (3.00)^{2}+\sqrt (5.00)_{y} (\sqrt (10.00)^{2}+\sqrt (6.00)^{2}}$
=0.882353 -> φ = $28.07^{\circ}$
(c)
cos φ=$ \frac{AxBx+AyBy}{AB}$
=$\frac{(-4.00) (7.00)+(2.00)(14.00)}{(\sqrt (-4.00)^{2}+\sqrt (2.00)_{y} (\sqrt (7.00)^{2}+\sqrt (14.00)^{2}}$
=0 -> φ = $90^{\circ}$
