1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)


    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:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook