Help me calculate magnitudes and components of vectors?

Question

The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.

Here is the diagram:

http://capa.hep.uprm.edu/msuphysicslib/Graphics/Gtype07/prob01a_vectors2.gif

DATA:

alpha=48.7°;

beta=57.6°;

|A|=5.30 cm.

The vector A - B is parallel to the -x axis (points due West).

Calculate the y-component of vector B.

Calculate the x component of the vector A -B.

Calculate the magnitude of the vector A + B.

If I were to move the vectors to the center, does its angle change?

Answer 1

A - B is parallel to the -x axis

so

A*sin(alpha)=B*cos(beta)

5.3*sin(48.7)=|B|*cos(57.6)

|B|=7.4309

By=-|B|*cos(57.6) j=-3.9817 (j)

(A-B)x=Ax - Bx=

-|A|*cos(48.7) - |B|*sin(57.6)=

=-9.7722 (i)

|A+B|=square((Ax+Bx)^2 + (Ay+By)^2)

=square((7.7068+63.4153))

=8.4334 (Cm)

No

Because they are free vectors.

Answer 2

One of the primary rules of vectors is that you may translate the vector parallel to itself and it remains the same vector. So yes move them to the center