When Studying Vectors, How Would I Go About Answering This Question?

Question

In Each of the following Cases, find the magnitude and direction of the resultant vectors of the two given vectors:

a) a displacement of magnitude 26km on a bearing of 175 degrees and a displacement of magnitude 18km on a bearing 294 degrees

b) Forces of 355 N on a bearing of 320 degrees and 270 N on a bearing of 025 degrees

help would be MUCH appreciated, if you could also explain how you answer it ?

also if you feel like drawing a diagram on paint or something if you could link it?

THANKS :D

Answer 1

in order to add vectors, it's necessary to convert to (x,y) from (r,θ)

For problem (a), we want to add

(26,175°) and (18,294°)
Now, bearings use 0° as North, measured clockwise, so we have to use

x = r*sinθ
y = r*cosθ

(26,175°) -> (2.266,-25.901)
(18,294°) -> (-16.444,7.321)
add 'em up to get
(-14.178,-18.580)
convert back to (r,θ) to get distance and bearing.

now go and do (b) the same way