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    Hi I was wondering if someone could explain to me the dot product of two vectors and how to go about finding A.B?

    I have attached a question which I found, but it doesn't follow the formula of A.B so I was confused as to how to go about these questions and was wondering if someone could explain it??
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    if

    A=a_{1}i+a_{2}j+a_{3}k,  B=b_{1}i+b_{2}j+b_{3}k, A.B= (a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3  })

    https://math.dartmouth.edu/archive/m...m9lect1031.pdf

    the b) and c) are for the cross product and the area of a parallelogram formed by 2 vectors.
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    The formula is: \boldsymbol{a} \cdot \mathbf{b}=(a_{1},a_{2},a_{3}) \cdot (b_{1},b_{2},b_{3})=a_{1}b_{1}+a  _{2}b_{2}+a_{3}b_{3}

    This is exactly what has happened in part a. So I'm not sure what you mean by it doesn't follow the formula?

    Do you mean it doesn't follow: \boldsymbol{a}\cdot \mathbf{b}=|\boldsymbol{a}|| \boldsymbol{b} |cos\Theta
    ?
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    (Original post by rayquaza17)
    The formula is: \boldsymbol{a} \cdot \mathbf{b}=(a_{1},a_{2},a_{3}) \cdot (b_{1},b_{2},b_{3})=a_{1}b_{1}+a  _{2}b_{2}+a_{3}b_{3}

    This is exactly what has happened in part a. So I'm not sure what you mean by it doesn't follow the formula?

    Do you mean it doesn't follow: \boldsymbol{a}\cdot \mathbf{b}=|\boldsymbol{a}|| \boldsymbol{b} |cos\Theta
    ?

    Yes that's what I meant. It didn't follow the second formula. Am I correct in presuming, that if an angle has not been indicated I use

    And when an angle is indicated I use


    Sorry this may sound stupid it's just vectors are my least favorite topic in maths!
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    (Original post by Sapphiresmith)
    Yes that's what I meant. It didn't follow the second formula. Am I correct in presuming, that if an angle has not been indicated I use

    And when an angle is indicated I use


    Sorry this may sound stupid it's just vectors are my least favorite topic in maths!
    That's correct.

    Don't worry, I hated vectors at a level too. Now I'm at uni though, they're one of my favourite things.
 
 
 
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