How Do You Subtract Vectors and Determine Their Direction?

[klm]

vector A = 7i + 4J
vector B= -4i - 8j
vector F = vector A - 3B

are you allowed to do this:
Fx= Ax - 3Bx : 7-3(-4) =19
Fy= Ay -3By : 4- 3(-8) = 28
or is there some rule to get the 3b?

and then how do you get the direction? when i do tan^-1 (28/19) = 55.8 . but how can i tell what quadrant vector F is in? i know vector A is in quad 1. and B is in quad 3. but since i am subtracting vector B, it is really going in quad 1? so is vector F really in quad 1?
sorry for all the questions!

 

[genneth]

Get some graph paper, and draw it! Draw A, B, -3B and F. Can you see what the numbers are actually representing as geometry?

It should be obvious which quadrant things are in... if x and y are both positive, they're in the first quadrant... I'll let you fill in the conditions for the other three.

 

[klm]

i did draw it already.
i know A is in quad 1.
B is in quad 3, but since i am subtracting ( i have to take the opposite vector) it would be in quad 1 as well.
so vector F should be in quad 1 correct?

 

[genneth]

Yes. You can also see it from the graph. Or, by noting that the defining of a vector in quadrant 1 is that both x and y components are positive. Can you generalise that definition for the other quadrants?

 

[dynamicsolo]

vector A = 7i + 4J
vector B= -4i - 8j
vector F = vector A - 3B

are you allowed to do this:
Fx= Ax - 3Bx : 7-3(-4) =19
Fy= Ay -3By : 4- 3(-8) = 28
or is there some rule to get the 3b?

Your components look to be correct. You can calculate each component algebraically as you have done.

and then how do you get the direction? when i do tan^-1 (28/19) = 55.8 . but how can i tell what quadrant vector F is in? i know vector A is in quad 1. and B is in quad 3. but since i am subtracting vector B, it is really going in quad 1? so is vector F really in quad 1?

Both components of F are positive, so what quadrant does that put it in?

(I just spotted your later response. Your graph seems to confirm the algebra.)

 

[klm]

^thank you both! i just needed to make sure that you are allowed to find components like that. by multiplying the 3 with the B component. thanks!