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Homework Help: Multiplying vectors

  1. Feb 13, 2010 #1
    If a = t^2 i - (4-t)j
    and b = i + t j
    show d/dt (a.b) = (a x db/dt) + (da/dt x b)


    I know you have to multiply the vectors a and b
    then do da/dt
    then db/dt
    and times db/dt with a
    and times da/dt with b
    that should be the proof

    However, I don't know how to multiply the vectors!
    Can someone please tell me how to multiply them

    Thank you, in advance
     
  2. jcsd
  3. Feb 13, 2010 #2
    There are two products defined over three dimensional vectors.

    First is the inner (\dot\scalar) product, that for any a=(a1,a2,a3), b=(b1,b2,b3)
    Gives

    a.b=a1*b1+a2*b2+a3*b3.

    Which means, multiply the vector component-wise and then sum up the results. This product gives a number!

    The second is the vector (\cross) product

    which is:

    [tex]\vec{a} X \vec{b}=(a_{2}b_{3}-b_{2}a_{3})\hat{i}+(a_{3}b_{1}-a_{1}b_{3})\hat{j}+(a_{1}b_{2}-a_{2}b_{1})\hat{k}[/tex]

    The result is a vector!

    Now please be careful. The identity which you are trying to prove involves only dot products. So it's:

    [tex]\frac{d}{dt}(\vec{a}.\vec{b})=\vec{a}.\frac{d}{dt}\vec{b}+\vec{b}.\frac{d}{dt}\vec{a}[/tex]
     
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