Let (vec{A}=left(3.0 mathrm{~m}, 20^{circ} ight.) south of east ()), (vec{B}=(2.0 mathrm{~m}), north ()), and (vec{C}=left(5.0 mathrm{~m}, 70^{circ}

Let \(\vec{A}=\left(3.0 \mathrm{~m}, 20^{\circ}\right.\) south of east \()\), \(\vec{B}=(2.0 \mathrm{~m}\), north \()\), and \(\vec{C}=\left(5.0 \mathrm{~m}, 70^{\circ}\right.\) south of west \()\).

a. Draw and label \(\vec{A}, \vec{B}\), and \(\vec{C}\) with their tails at the origin. Use a coordinate system with the \(x\)-axis to the east.

b. Write the \(x\) - and \(y\)-components of vectors \(\vec{A}, \vec{B}\), and \(\vec{C}\).

c. Find the magnitude and the direction of \(\vec{D}=\vec{A}+\vec{B}+\vec{C}\).