# vectors problem #3

• Oct 1st 2007, 02:00 AM
afeasfaerw23231233
vectors problem #3
• Oct 1st 2007, 02:57 AM
earboth
Quote:

Originally Posted by afeasfaerw23231233

hello,

you have almost finished:
$\displaystyle \theta = \arccos(\cos(\theta)) = \arccos\left( \frac{\vec{u} \cdot \vec{v}}{|\vec{u}| \cdot |\vec{v} |} \right)$

That's it!
• Oct 1st 2007, 04:56 AM
afeasfaerw23231233
well, but the answer in my textbooks says theta is 120 degree!!
how can i get 120 degree from this?
• Oct 1st 2007, 05:53 AM
topsquark
Quote:

Originally Posted by afeasfaerw23231233
well, but the answer in my textbooks says theta is 120 degree!!
how can i get 120 degree from this?

u and v are unit vectors, so |u| = |v| = 1.

We are also told that u + v is a unit vector, so
$\displaystyle (u + v) \cdot (u + v) = |u + v|^2 = 1$
(Since for any vector x, $\displaystyle x \cdot x = x^2$.)

But
$\displaystyle (u + v) \cdot (u + v) = u^2 + v^2 + 2 u \cdot v$

What can you make of all this?

-Dan
• Oct 1st 2007, 06:33 AM
afeasfaerw23231233
oh, i know it now. thanks!