# Thread: Finding magnitude of u + v help?

1. ## Finding magnitude of u + v help?

Hey all!

I was taking a quiz for my trig class and the following problem came up:

Find the sum of u + v, given that |u| = 16, |v| = 16, and Theta = 106°.

The magnitude of u + v is:
19.3

The resultant vector u + v makes the angle
53.0 with u.

When I tried the problem, I got 22.6 for the magnitude and 45
° for the angle.

I thought that r = sqrt(u^2 + v^2), and I could use arctan=(16/16) to find the angle (at least that's what my math teacher had said).

Any help on how they got these solutions?

2. ## Re: Finding magnitude of u + v help?

Doing what you have done only works if the vectors are at right angles to each other, which these aren't. (Basically, you have used the Pythagoras theorem.)
Draw a diagram with the two vectors angled at 106 degrees to each other and draw in the vector u + v. Use the cosine rule to calculate the magnitude of u + v followed by the sine rule to calculate the angle.

3. ## Re: Finding magnitude of u + v help?

Originally Posted by ktelyn
Hey all!
I was taking a quiz for my trig class and the following problem came up:
Find the sum of u + v, given that |u| = 16, |v| = 16, and Theta = 106[FONT=arial]°.
The magnitude of u + v is:
19.3[COLOR=#0000ff]
$\displaystyle \|u+v\|^2=\|u\|^2+\|v\|^2-2\|u\|\|v\|\cos(74^o)$
Using the law of cosines and the supplement of the angle between $\displaystyle u~\&~v.$

4. ## Re: Finding magnitude of u + v help?

I think I know what I did wrong, LOL!

I thought I had to put the angle they provided for the cosA part, but in reality I have to use the supplement.

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### find the magnitude of u Ă— v

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