4. If \( \|\vec{u}\|=13,\|\vec{v}\|=8 \), and the direction of \( \vec{u} \) is \( 55^{\circ} \), and the direction of \( \vec{v} \) is \( 155^{\circ} \) : a. Find the component form of \( \vec{u} \) and \( \vec{v} \). Round to the nearest hundredth.

To find the component form of the vectors \( \vec{u} \) and \( \vec{v} \), you can use the formulas for the components based on their magnitudes and angles. For \( \vec{u} \): \[ \vec{u} = \|\vec{u}\| (\cos(55^{\circ}), \sin(55^{\circ})) = 13 (\cos(55^{\circ}), \sin(55^{\circ})) \] Calculating the components: \[ \cos(55^{\circ}) \approx 0.5736, \quad \sin(55^{\circ}) \approx 0.8192 \] Thus, \[ \vec{u} \approx 13 (0.5736, 0.8192) \approx (7.46, 10.65) \] For \( \vec{v} \): \[ \vec{v} = \|\vec{v}\| (\cos(155^{\circ}), \sin(155^{\circ})) = 8 (\cos(155^{\circ}), \sin(155^{\circ})) \] Calculating the components: \[ \cos(155^{\circ}) \approx -0.9063, \quad \sin(155^{\circ}) \approx 0.3907 \] Thus, \[ \vec{v} \approx 8 (-0.9063, 0.3907) \approx (-7.25, 3.13) \] So, the component forms are \( \vec{u} \approx (7.46, 10.65) \) and \( \vec{v} \approx (-7.25, 3.13) \).