The route followed by a hiker consists of three displacement vectors $\vec{A}$, $\vec{B}$, and $\vec{C}$. Vector $\vec{A}$ is along a measured trail and is 2770 m in a direction $26.0^\circ$ north of east. Vector $\vec{B}$ is not along a measured trail, but the hiker uses a compass and knows that the direction is $18.0^\circ$ east of south. Similarly, the direction of vector $\vec{C}$ is $26.0^\circ$ north of west. The hiker ends up back where she started, so the resultant displacement is zero, or $\vec{A} + \vec{B} + \vec{C} = 0$. Find the magnitudes of (a) vector $\vec{B}$ and (b) vector $\vec{C}$.
(a) Number
Units m
(b) Number
Units m