How Do You Calculate the Components of Vector C?

[donking225]

1. Vector A has x and y components of −20 cm and 19 cm, respectively; vector B has x and y components of 11.1 cm and −20 cm, respectively. If A−B +3 C = 0, what are the x and y components of vector C ?


2. Not too sure. I am thinking that using trigonometry or Pythagorean theorem.


3. I attempted to find vector A and B by using Pythagorean theorem, which I roughly get to be 27.6 and 22.9. I am unsure how the negative values of the x and y components affect the actual number for the vectors. I know that I could also find the angles of the vectors using trig, but as stated earlier I am unsure how negative x and y components affect the magnitude of the vector except for it going in a different direction. After I know all that information I still do not know how to solve for the components of vector C. I am still relatively new with vectors so it would be great if you could explain things in the simplest terms possible.Thanks

 

[voko]

When you add vector A to vector B, what happens with their components?

 

[HallsofIvy]

I don't see any reason to use "trigonometry or Pythagorean theorem." In particular, when you say "I attempted to find vector A and B by using Pythagorean theorem, which I roughly get to be 27.6 and 22.9" it sounds like you really do not know what a vector is. The numbers you got from the Pythagorean theorem are the lengths of the vectors which is just on aspect of a vector, not the vector itself.

You are given components so do everything in components.

"Vector A has x and y components of −20 cm and 19 cm" so A= -20i+ 19j.
"vector B has x and y components of 11.1 cm and −20 cm, respectively" so B= 11.1i- 20j.

If we write C as Xi+ Yj, then A+ B+ 3C= -20i+ 19j+ 11.1i- 20j+ 3Xi+ 3Yj= (-20+ 11.1+ 3X)i+ (19- 20+ 3Y)j= 0i+ 0j. Solve those two equations for X and Y.