Vector A⃗ points in the negative x direction. Vector B⃗ points at an angle of 32.0∘ above the positive x axis. Vector C⃗ has a magnitude of 18m and points in a direction 43.0∘ below the positive x axis.Given that A⃗ +B⃗ +C⃗ =0, find the magnitudes of A⃗ and B⃗ .

Question

Vector A⃗  points in the negative x direction. Vector B⃗  points at an angle of 32.0∘ above the positive x axis. Vector C⃗  has a magnitude of 18m and points in a direction 43.0∘ below the positive x axis.Given that A⃗ +B⃗ +C⃗ =0, find the magnitudes of A⃗  and B⃗ .

anonymous · Answer

would anyone be so kind to assist?

anonymous · Answer

Let's denote the x direction as i and y direction as j.

We will actually get 2 equations:
-A + B*cos(32) + 18*cos(-43) = 0 [along X direction]   (1)
B*sin(32) - 18*sin(43) = 0 [along Y direction].              (2)

I guess you have some problem trying to solve this equation. Are you allowed to use a calculator?? If yes, then it's done, else it's a little complicated.

anonymous · Answer

to work out the magnitudes of A and B can I use the following equations?
B= C*sin(43) / sin(32)
A= B*cos(32)+ C*cos(43)?

anonymous · Answer

Yes, one way would be to use a calculator to compute sin(43) and cos(32). For that you can always use an online scientific calculator (if you don't have one with you). Since C =18, you get the value of B, which you can use in the other equation  to get A.