# Find the angle between the two vectors

1. Aug 28, 2011

### skysunsand

1. The problem statement, all variables and given/known data
What is the angle between vectors E and F in the diagram?
Use components to determine the magnitude and direction of G= E+F

2. Relevant equations

sqrt(x^2 + y^2) is the equation for magnitude

3. The attempt at a solution

All right. Given by the diagram that the end point of F is (-1,-2), I calculated that F's magnitude would be sqrt(5). Given E's diagram, its end point is (1,1), so its magnitude was calculated to be sqrt(2).

Then since I have opposite and adjacent calculations, I would use tangent-
tan (theta) = sqrt(2)/sqrt(5), and then take the arc tangent of that to get an answer of 35.9...which is wrong. Why?

In regard to the second question about G, I am stumped. How do you add vectors together? Do you just add their coordinates?

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2. Aug 28, 2011

### rock.freak667

F = (-1,2)

Yes you would add together the corresponding components.

3. Aug 28, 2011

### skysunsand

Whoops. But either way, that doesn't change the fact that it turns out to be sqrt(5), and I'm still getting the wrong answer....

4. Aug 28, 2011

### skysunsand

Well that went well, I got the magnitude correct as 3.00, but then how would I figure out the direction of G? All I know is G's end point.

5. Aug 28, 2011

### rock.freak667

Yes but you need to add together the angles between the individual vectors and the y-axis. By chance, do you know how to calculate the dot product of two vectors?

Well what is the end point of G?

6. Aug 28, 2011

### skysunsand

Why would I have to do vectors F and E separately? Can't I just draw a line between them, call that the hypotenuse, and use my magnitudes that I found? I don't even know what a dot product is... so I guess that answers your question!!

The end point of G is (0,3), which I would think would give me a right angle from the origin, but that's definitely not the right answer.

7. Aug 28, 2011

### PeterO

A right angle would be fine if you are considering the angle with the positive x axis.

8. Aug 28, 2011

### skysunsand

All right, that was correct, and that makes sense because its coordinates were directly up the y-axis. But what of the two vectors that I have to find the angle of? Why is arctan not working for my values?

9. Aug 28, 2011

### PeterO

That 35.9 degrees you got may be tha angle between the y-axis and the vector, so you have to add an extra 90 to get the base reference.

I seem to recall we base vectors on polar co-ordinates, so there is just a single ray for the measurement [like the positive x-axis] and an angle from that ray, with anticlockwise taken as positive.

10. Jan 29, 2013

### chicagobears34

don't mean to necro this thread, but i am very confused on how to find the angle between the vectors (phi). how do u do that?

11. Jan 29, 2013

### Staff: Mentor

tangent of theta is not sqrt(2)/sqrt(5). For this to be correct, these must be the opposite and adjacent sides of the same right triangle. I don't see any such right triangle in the figure. What is the angle between E and the y axis? What is the angle between F and the y axis. The sum of these two angles is the angle between E and F.

12. Jan 29, 2013

### chicagobears34

all that was given was in the picture attached to the OP's post.
Only the magnitudes could be calculated. nothing was really given

13. Jan 29, 2013

### PeterO

Just as you could use the co-ordinates on the original figure to get the magnitude of each vector, you could use those same co-ordinates to calculate the angles mentioned by "Chestermiller".
Actually you should be able to recognise the size of one of the angles - as you will (should) have come across it so many times before.

14. Jan 30, 2013

### PeterO

I hope you have appreciated that finding the angle between the two vectors and the magnitude of the sum of the vectors are two quite independent questions.