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Find the angle that the vector R

part 1 of 2
Two vectors A and B, are lying in the xy
plane and given by
A = Axi +Ayj
B = Bxi +Byj
(x y are subscripts)

where A x = 4.4 m, A y = 1.74 m, B x = 7.58 m, B y = -6.76 m. Let R = A+B.
Find the magnitude of R. Answer in units
of m.

So it is
A = 4.4mI + 1.74mJ
B = 7.58mI - 5.02J

I have found out R by using the distance formula
sqrt(11.98^2 + 5.02^2) = 12.9893 m(which is right)

part 2 of 2
Find the angle that the vector R makes from
the positive x axis. Choose your answer to be
between -180 # and +180 # . The positive an_
gular direction is counter clockwise measured
from the x axis. Answer in units of # .

I tried this problem using the cosine law.
-5.02squared-11.98squared-12.99squared
______________________________________(division)
-2*11.98*12.99

I got 22.73 degrees. But when I sumbit this answer, it says I'm wrong. Can you figure out what I'm doing wrong?
 

HallsofIvy

Science Advisor
Homework Helper
41,709
876
The angle you are looking for, the angle the vector R makes with the x-axis is NOT an angle in the triangle formed by the three vectors. Also, you have the cosine law wrong (it may be a typo).
It is a^2= b^2+ c^2- 2bc cos(A) so cos(A)= (a^2- b^2- c^2)/(2bc).

In any case, the simplest way to do this is to look at the vector
R only. You know the components of R. Look at the right triangle formed by the vector and it's components and think "tangent"!
 

enigma

Staff Emeritus
Science Advisor
Gold Member
1,738
9
Originally posted by NINHARDCOREFAN
where A x = 4.4 m, A y = 1.74 m, B x = 7.58 m, B y = -6.76 m. Let R = A+B.
Find the magnitude of R. Answer in units
of m.

So it is
A = 4.4mI + 1.74mJ
B = 7.58mI -5.02J
By is incorrect (it's the y-comp of R), but it looks like you caught that in the next part.

I have found out R by using the distance formula
sqrt(11.98^2 + 5.02^2) = 12.9893 m(which is right)

part 2 of 2
Find the angle that the vector R makes from
the positive x axis. Choose your answer to be
between -180 # and +180 # . The positive an_
gular direction is counter clockwise measured
from the x axis. Answer in units of # .

I tried this problem using the cosine law.
-5.02squared-11.98squared-12.99squared
______________________________________(division)
-2*11.98*12.99

I got 22.73 degrees. But when I sumbit this answer, it says I'm wrong. Can you figure out what I'm doing wrong? [/B]
Just find the arctan. rise/run = tan θ , so atan (rise/run) = θ

Be sure you know what quadrant you're in. atan is only defined for +- 90 degrees, so you will need to add 180 degrees if you're in the second or third quadrants.
 
After I did that I got 22.74, the same answer as I did before, which is wrong.
 
The answer was -22.74(QIV), which is same as 22.74(QI)
 

HallsofIvy

Science Advisor
Homework Helper
41,709
876
Why is "-22.74(QIV)" the same as "22.74(QI)"? They look very different to me!
 
I figured that out last night, I thought the problem said that answer has to be between 0 and 180 but then realized that it was between -180 and 180.
 

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