A hiker follows a route that consists of three displacement vectors A, B, and C. Vector A is along a measured trail and is 1550 meters in a direction 25 degrees north of east. The direction of Vector B is 41 degrees east of south, and the direction of vector C is 35 degrees north of west. The hiker ends up back where at the original starting point, so the reslultant displacement is zero or A+B+C=0. Find the magnitudes of Vectors B and C.

Question

A hiker follows a route that consists of three displacement vectors A, B, and C.  Vector A is along a measured trail and is 1550 meters in a direction 25 degrees north of east.  The direction of Vector B is 41 degrees east of south, and the direction of vector C is 35 degrees north of west.  The hiker ends up back where at the original starting point, so the reslultant displacement is zero or A+B+C=0.  Find the magnitudes of Vectors B and C.

An explanation of the answer with some work would be greatly appreciated.  Thanks.

bobpursley · Answer

Break each of the vectors into N, E components.

For instance:
vectorC is -C*Cos35 E and C*sin35N
do that for all three vectors, then the sum of all three E vectors will be zero, and the sum of all three N vectors will be zero. Solve B, C (B,C is a magnitude of vectors b, C