Solving Vector Problem: Magnitude of R & r, Angle with x-axis

[deaninator]

Homework Statement

Consider the two vectors r1 and r2 shown in the diagram. The magnitudes of the two vectors are: r1=6.1 and r2=9.3. The vectors directions relative to the x-axis are defined by the angles: θ1=25 degrees and θ2=51 degrees.

What is the magnitude of the vector R=r1+r2?

What is the magnitude of the vector r=r2−r1?

What is the angle between R and the x axis? (in degrees)

What is the angle between r and the x axis? (in degrees)

Homework Equations

Picture is attached

The Attempt at a Solution

For vector R, I think the magnitude is 15.4
For vector r, I think the magnitude is 3.2
But how do i figure out the other 2?

Thanks a million once again!

 

[brewAP2010]

For the first question i also got 15.4, i got a different answer for the second question. The way that i solved this was i broke each vector into components, then i added or subtracted as indicated by the problem. For example to get 15.4 i broke r1 into x=5.53 and y=2.58, and I broke r2 into x=5.85 and y=7.23. I then added the x's and y's to get x=11.83 and y=9.81. I used these values to set up a triangle, and then used pythagorean theorem to solve R. Do the same thing for the second problem except subtract the components rather than adding them. I found the angles using the arctan of the opposite over the adjacent in each triangle. I hope this helps.

 

[deaninator]

For the first question i also got 15.4, i got a different answer for the second question. The way that i solved this was i broke each vector into components, then i added or subtracted as indicated by the problem. For example to get 15.4 i broke r1 into x=5.53 and y=2.58, and I broke r2 into x=5.85 and y=7.23. I then added the x's and y's to get x=11.83 and y=9.81. I used these values to set up a triangle, and then used pythagorean theorem to solve R. Do the same thing for the second problem except subtract the components rather than adding them. I found the angles using the arctan of the opposite over the adjacent in each triangle. I hope this helps.

Ok 15.4 according to the computer is incorrect. Do you have to break down the vectors to components? Like my teacher assigned this problem but in class we never touched base on how to break down vectors.

 

[yjresources]

Here are my solutions. Hope it helps!

 

[deaninator]

Here are my solutions. Hope it helps!

Thanks it really did! But how did you get the magnitude of ''r'' to be 8.5? I keep getting 4.66

 

[yjresources]

Oh yeah... you're right. I made a mistake punching the numbers in my calculator, so r = 4.66 Glad to have helped.