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Math Help - Vector question - any hints welcome

  1. #1
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    Vector question - any hints welcome

    Ok, if I know that 3 \vec c = \vec a + 2 \vec b and \vec d = - \vec a + 2 \vec b and that | \vec a | = 2 | \vec b |. (o is origin)

    How do I prove that |<cod| = \frac{ \pi }{2} ?

    Any hints would be extremely helpful here. Thanks in advance.
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  2. #2
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    Quote Originally Posted by FreeT View Post
    Ok, if I know that 3 \vec c = \vec a + 2 \vec b and \vec d = - \vec a + 2 \vec b and that | \vec a | = 2 | \vec b |. (o is origin)

    How do I prove that |<cod| = \frac{ \pi }{2} ?

    Any hints would be extremely helpful here. Thanks in advance.
    show that the dot product of vector c and vector d = 0
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  3. #3
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    Thanks, I did ( \frac {\vec a}{3} + \frac {2 \vec b}{3}).( - \vec a + 2 \vec b) and said that \vec a= x_1 i + y_1 j and that \vec b= x_2 i + y_2 j

    It worked down to 1/3 (|x_1|^2 - |y_1|^2) + 4/3 (|x_2|^2 + |y_2|^2) and now I need to prove this equal to zero.
    Sorry to ask, but can anyone help?
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  4. #4
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    You are making it far too hard. All we need do is:
    \left( {\overrightarrow a  + 2\overrightarrow b } \right) \cdot \left( { - \overrightarrow a  + 2\overrightarrow b } \right) =  - \overrightarrow a  \cdot \overrightarrow a  + 4\overrightarrow b  \cdot \overrightarrow b  =  - \left\| {\overrightarrow a } \right\|^2  + 4\left\| {\overrightarrow b } \right\|^2  = ?
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  5. #5
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    Thanks so much. (Vectors has never been my strong point )
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