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Math Help - Vector problem

  1. #1
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    Vector problem

    Greetings,
    I am struggling with a problem and I would appreciate if someone would explain how should I solve the following problem. "Angle between vector A and vector B is 120 degrees. |a|=3; |b|=4. What is the result of (3a-2b)*(a+2b)?"

    Thank you in advance,
    Kostas.
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  2. #2
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    Re: Vector problem

    Quote Originally Posted by Kostass View Post
    Greetings,
    I am struggling with a problem and I would appreciate if someone would explain how should I solve the following problem. "Angle between vector A and vector B is 120 degrees. |a|=3; |b|=4. What is the result of (3a-2b)*(a+2b)?"
    $\vec{A} \cdot \vec{B} = \left\| \vec{A} \right\|\left\| \vec{B} \right\|\cos \left( {\dfrac{{2\pi }}{3}} \right)$
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  3. #3
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    Re: Vector problem

    Hello, Kostass!

    \text{Angle between }\vec{a} \text{ and }\vec{b}\text{ is }120^o. \;\;|a|=3;\;|b|=4.

    \text{Find: }\:(3a-2b)\cdot(a+2b)

    Preliminary calculations:

    a^2 \:=\:|a|^2 \:=\: 3^2 \quad\Rightarrow\quad a^2 \:=\: 9

    b^2 \:=\:|b|^2 \:=\:4^2 \quad\Rightarrow\quad b^2 \:=\:16

    \cos\theta \:=\:\frac{a\cdot b}{|a||b|} \;\;\;\Rightarrow\;\;\; \cos 120^o \:=\:\frac{a\cdot b}{3\cdot 4} \;\;\;\Rightarrow\;\;\; a\cdot b \:=\:12(\text{-}\tfrac{1}{2}) \;\;\;\Rightarrow\;\;\; a\cdot b \:=\:\text{-}6



    (3a-2b)\cdot(a + 2b) \;=\; 3a^2 + 4ab - 4b^2

    . . . . . . . . . . . . . . =\;3(9) + 4(\text{-}6) - 4(16)

    . . . . . . . . . . . . . . =\;27 - 24 - 64

    . . . . . . . . . . . . . . =\;-61
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