PHYSICS-Vector Problem?

Question

"Vector A has x and y components of -8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and -6.60 cm, respectively. If A-B+3C=0, what are the components of C."

Am I doing this correctly??? I know that one normally groups the x and y components of each vector into i hat and j hat to add them...so, if it were just asking what A+B is equal to , I would (-8.70+13.2)i hat+(15.0+(-6.60))j hat to get 4.5i hat+8.9 j hat. Since there is now this 3C component, do I just set 3C=-4.5 to get -1.5 & 3C=-8.9 to get -2.97, or this just totally wrong??? Would my final answer be for Vector C that x=-1.5 and y=-2.97???

Thanks!!

Answer 1

make it simpler
C = (1/3) [B - A] ---------- (1)
----------------------------------
B - A = (13.2 i - 6.60 j) - (- 8.70 i +15 j)
B - A = (13.2 + 8.70) i - (6.60 + 15) j
B - A = 21.9 i + (- 21.6) j --------- (2)
------------------------------------
put (2) in (1)
C = (1/3) [21.9 i + (- 21.6) j ]
C = [7.3 i + (- 7.2) j ] = Cx i + Cy j
components of C are
Cx = 7.3 cm
Cy = - 7.2 cm

Answer 2

You're sort of on the right track, but you've got some plus and minus signs mixed up. It looks like by doing the calculations you describe, you're solving "A + B = 3C"; but this is not the equation you're asked to solve.

I think you're making it too hard. Remember that you can treat all the "x" components in one equation and all the "y" components in a separate equation:

A_sub_x – B_sub_x + 3C_sub_x = 0
A_sub_y – B_sub_y + 3C_sub_y = 0

You're given the x and y components for A and B, so just plug into those equations and solve for the x & y components of C.