The x and y components of a vector A are 4 and -5 respectively and Vector B are -2 and 1 respectively. If A-B+3C=0, find the Cartesian coordinates for vector C?

Answer 1

(4-(-2)+3Cx)i + (-5-1+3Cy)j=0

check that, then solve for Cx

4+4=-3Cx or Cx=-8/3
-5-1=-3Cy
Cy=2

check all that, I did it in my head.

Answer 2

A=4x-5y
B=-2x+1y
--------
6x-6y

But A-B+3C=0
therefore, 3C= A-B
--- ---
3 3

C= A-B
---
3

But A-B = 6x -6y

therefore, A-B
the ---
3

6x-6y
-----
3

= 2x-2y

Therefore, C= 2×-2y

Answer 3

A=4x-5y
B=-2x+1y
--------
6x-6y

But A-B+3C=0
therefore,

C= A-B
---
3

But A-B = 6x -6y

therefore,

6x-6y
-----
3

= 2x-2y

Therefore, C= 2×-2y