How Do You Calculate Vector Sums and Differences?

[armolinasf]

Homework Statement

find the vector sum of A + B. Find the vector difference of A-B. Then find the magnitude and direction -A-B and B-A.

Vector A=12m and B=18m and the angle between B and the x-axis is 37 degrees.

I'm really confused about how to think about a vector and if i should just treat them like triangle or what. Help is much appreciated Thanks!

The Attempt at a Solution

 

[SteamKing]

What is the definition of a vector?

 

[armolinasf]

a magnitude in a given direction.

If i wanted to find the sum of a+b would i be looking for the third side of a triangle with sides 12 and 18 and with an angle of 37 degrees between them?

 

[armolinasf]

if I were to do it by components components of A would be Ax=-12 Ay=0 and Bx=18cos37=14.4 and By=18sin37=10.8. then Sx=-12+14.4=2.4 and Sy=10.8.

then S=sqrt(2.4^2+10.8^2)=11.06 would this be the correct magnitude?

 

[HallsofIvy]

You don't have to use components and the fact that the original vectors are not given in terms of components suggests that you are not supposed to. If you draw A, the B attached to the "tip" of A, the line from the base of A to the tip of B is A+ B and forms a triangle.

However this

Vector A=12m and B=18m and the angle between B and the x-axis is 37 degrees.

makes no sense. You are given B as magnitude and direction but you are only given the magnitude of A. Are you not given a direction for A? In your last post, you seem to be assuming that A is in the direction of the x-axis. Are you explicitely given that?

IF that is true, then the angle between vectors A and B, the angle in the triangle formed by A, B, and A+ B, is 180- 37= 143 degrees. You can use the cosine law to find the magnitude (length) of the third side, A+ B. After that, you could use the sine law to find the angles.

 

[armolinasf]

okay so if i use the cosine rule C^2=12^2+18^2-12*18*cos(147) I get 25.3 and then using the sine rule sin147/25.3=sinx/18 i get x=22.8 would that be the direction then?