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Math Help - vectors problem #3

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    vectors problem #3

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    Quote Originally Posted by afeasfaerw23231233 View Post
    hello,

    you have almost finished:
    <br />
\theta = \arccos(\cos(\theta)) = \arccos\left( \frac{\vec{u} \cdot \vec{v}}{|\vec{u}| \cdot |\vec{v} |} \right)

    That's it!
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    well, but the answer in my textbooks says theta is 120 degree!!
    how can i get 120 degree from this?
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    Quote Originally Posted by afeasfaerw23231233 View Post
    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
    (u + v) \cdot (u + v) = |u + v|^2 = 1
    (Since for any vector x, x \cdot x = x^2.)

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

    What can you make of all this?

    -Dan
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  5. #5
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    oh, i know it now. thanks!
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