Vector A+B and A-B: Graphical Method

[Propagandhi]

Homework Statement

Vector A has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x axis. Using graphical methods, find (a) the vector sum A + B and (b) the vector difference A - B.

Homework Equations

sine,cosine,tangent, A= Axi+Ayj, B=Bxi+Byj (x and y are subscripts)

 

[Kurdt]

I'm not sure what you are thinking of with you attempt. The question asks you to use graphical techniques. Are you familiar with the triangle rule or parallelogram rule of vector addition?

 

[Propagandhi]

Those don't ring a bell. How would I go about doing one of these?

 

[Kurdt]

These are graphical representations of adding vectors. You take the first vector and draw the second vector from the point of the first. The resultant vector is the sum of the first two and is from the origin of the first to the tip of the second. See here for a pictorial representation and more information:

http://mathworld.wolfram.com/ParallelogramLaw.html

 

[Propagandhi]

so using that, how would I go about solving this problem?

 

[Kurdt]

Its a case of a fair bit of geometry. Try setting up the axes and solving for the angle and magnitude of the resultant vector. Also note that a vector difference is the same as a vector sum with the second vector multiplied by -1. That is:

$$\mathbf{A}-\mathbf{B} = \mathbf{A} + (-\mathbf{B})$$