# Finding magnitude of u + v help?

• Nov 9th 2012, 06:01 AM
ktelyn
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?
• Nov 9th 2012, 06:35 AM
BobP
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.
• Nov 9th 2012, 06:52 AM
Plato
Re: Finding magnitude of u + v help?
Quote:

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]

$\|u+v\|^2=\|u\|^2+\|v\|^2-2\|u\|\|v\|\cos(74^o)$
Using the law of cosines and the supplement of the angle between $u~\&~v.$