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Math Help - dot product verification

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    Question dot product verification

    is the dot product of (a+b) . (a + b) = a^2 + b^2 + 2ab ?
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    Quote Originally Posted by dopi View Post
    is the dot product of (a+b) . (a + b) = a^2 + b^2 + 2ab ?
    No, it's just a^2 + b^2.

    You only do componentwise multiplication with dot products.
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    Quote Originally Posted by dopi View Post
    is the dot product of (a+b) . (a + b) = a^2 + b^2 + 2a.b ?
    That is more or less correct!
    But it should be written as \left( {a + b} \right) \cdot \left( {a + b} \right) = a \cdot a + 2a \cdot b + b \cdot b.
    Please note that the ‘dot products’ in the answer.
    In fact here is an important form: \left( {a + b} \right) \cdot \left( {a + b} \right) = \left\| a \right\|^2  + 2a \cdot b + \left\| b \right\|^2

    Quote Originally Posted by Prove It View Post
    No, it's just a^2 + b^2.
    You only do componentwise multiplication with dot products.
    No that is not correct!
    To see where you went wrong, recall v \cdot \left( {u + w} \right) = v \cdot u + v \cdot w.
    Let v = \left( {a + b} \right)\;,\,u = a\;\& \,w = b and apply the distribution rule twice.
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