The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.
DATA: alpha = 42.7 degrees, beta = 56.8 degrees, A = 6.70 cm. The vector A - B is parallel to the -x axis (points due West). Calculate the y component of vector B.
i) Calculate the x component of the vector A -B
ii) Calculate the magnitude of the vector A + B
I used the following approach to get A and B but the CAPA online assignment system says its wrong.
A = (AxCos(α), AxSin(α))
B = (BxSin(β), BxCos(β))
we have α and A so we have the x and y components of A. then we know y component of (A-B) must be zero cause (A-B) is parallel to x-axis so we know the y-component of B (which is equal to y-component of A) so we say AxSin(α) = BxCos(β) and we get the magnitude of B now we can calculate the x-component of B as well as I followed:
A = (AxCos(α), AxSin(α)) = (6.70 x Cos(42.7), 6.70 x Sin(42.7)) = (-4.9239, -4.5436)
and y-component of B must be -4.5436 so
-4.5436 = B x Cos (56.8) => B = -4.5436/Cos(56.8) => B = 8.2978
and so B = (8.2978, -4.5436)
and so -B = (-8.2978, +4.5436)
would you please tell me were I am wrong?