A dog searching for a bone walks 2.10 m south, then 8.20 m at an angle 30.0° north of east, and finally 12.0 m west. Find the dog's resultant displacement vector (magnitude & direction)

Find the magnitude and direction of the sum of the three given vectors. Use rectangular components and standard angle.

The route followed by a hiker consists of three displacement vectors A,B ,c Cand . Vector  A is along a measured trail and is 1550 m in a direction 25.0° north of east. Vector B 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 C is 10.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or  A+  B+ C = 0. Find the magnitudes of vector B and vector C .

A hiker walks 2.5 miles in a direction 65° West of North, then 3.5 miles in a direction 40° South of West, then 1.5 miles due South. What must be the vector displacement of the hiker during the fourth part of the trip in order for the resultant to be 5.5 miles due West for the entire trip? Drawing a vector diagram or drawing individual vectors will help.