Find the angle between the two vectors

[skysunsand]

Homework Statement

What is the angle between vectors E and F in the diagram?
Use components to determine the magnitude and direction of G= E+F

Homework Equations

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

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?

 

[rock.freak667]

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).

F = (-1,2)

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

Yes you would add together the corresponding components.

 

[skysunsand]

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).

F = (-1,2)

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...

 

[skysunsand]

F = (-1,2)



Yes you would add together the corresponding components.

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.

 

[rock.freak667]

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...

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 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.

Well what is the end point of G?

 

[skysunsand]

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?

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.

 

[PeterO]

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.

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

 

[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?

 

[PeterO]

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?

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.

 

[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?

 

[Chestermiller]

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.

 

[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

 

[PeterO]

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

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.

 

[PeterO]

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?

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.