Question

Vector a has a magnitude of 5 m and is directed esast. Vector b has a magnitude of 4 m and is directed 35 degrees west of north. What are the (a) magnitude and (b) the direction of vector a + vector b?
What are the (c)magnitude and (e)direction of vector b - vecotr a?
(f) Draw a vector diagram for each combination.

My teacher ran out of time trying to explain this problem with us. And we are having a test on this kind of problem too. I was wondering how my teacher got these answers. All of the ways I have tried getting these answers I keep on getting the wrong numbers. Please help me.
a)4.2m
b)40 degrees east of north
c)8 m
d) 24 degrees north of west
e) How would I draw this?


Vector A is 5E
Vector B is 4 at 35W of N.
Change vector B to E,N
Vector B= 4N cos(360-35) + 4Esin(360-35)

This angle change is a simple way to keep it straight (cos from N clockwise is N component, Sin from N clockwise is E component).


Then convert Vector B
Vector B= 3.28N -2.29E

So, Vector A + B= 5E + 3.28N -2.29E
=2.71E + 3.28N

Magnitude = sqrt (2.71^2 + 3.28^2)
angle from N is arctan 2.17/3.28

I am not getting exactly the teachers answers, check my work, I or she could have made an error.