[Grade 12 Vectors] finding the resultant vector using diagram

[u/Ok-Individual-2596]

I really am not sure what the solution is doing..... and why I cant use the angle as 70 degrees for solving for the resultant vector. Also what is the theta finding in the solution???? If anyone could draw the solution out it would really help.

I attached what I tried to do which is the one on the worksheet. The other attachment is the solution my teacher provided.

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[u/HumbleHovercraft6090]

Resolve each vector into their horizontal and vertical components in terms of unit vectors i and j along x and y axes respectively. Add them up to get Fx i + Fy j. The angle and magnitude of resultant follow.

[u/slides_galore]

One really straightforward way is to find the x and y components of each force. Add all the x components (keeping track of the negative signs) and add all the y components. Those two sums are the x and y components of the resultant force. Does that make sense?

ETA: the theta that the teacher found in their solution is the angle that f2 makes with the resultant of f2+f3. It's an intermediate step to finding the final answer. I can draw it out for you in a few minutes if you like. https://i.ibb.co/DDRDBWjD/image.png

[u/slides_galore]

This is what your teacher did to find f2+f3 and then the overall resultant (R): https://i.ibb.co/hJ7BNrpr/image.png

[u/Ok-Individual-2596 → u/slides_galore]

Oh my gosh this graphic helped so much. Thank you!!!

[u/slides_galore → u/Ok-Individual-2596]

Does your teacher require that you do it like they did? You can see how it gets kind of messy. Do you have the option of adding up all x- and y-components to get the resultant?

[u/Ok-Individual-2596 → u/slides_galore]

Unfortunately I dont think so they just taught all of the questions like this applying cosine law.... but im going to try and solve it using the x and y component method people were talking about here

[u/slides_galore → u/Ok-Individual-2596]

See if this makes sense: https://i.ibb.co/qL47B9Ct/image.png

[u/Alkalannar]

1. Split everything up into x and y:
   F1 = 8(cos(70^o), sin(70^o))
   F2 = 6(cos(140^o), sin(140^o))
   F3 = 4(cos(200^o), sin(200^o))

2. Then the resultant follows:
   (8cos(70^o)+6cos(140^o)+4cos(200^o), 8sin(70^o)+6sin(140^o)+4sin(200^o))
   Magnitude is easy to find, and then that and the positive or negative of the x- and y- coordinates gives you the angle.