The route followed by a hiker consists of three displacement vectors , , and . Vector is along a measured trail and is 1550 m in a direction 24.0...

The route followed by a hiker consists of three displacement vectors , , and . Vector is along a measured trail and is 1550 m in a direction 24.0° north of east. Vector is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0° east of south. Similarly, the direction of vector is 19.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or + + = 0. Find the magnitudes of vector and vector .