Results 1 to 7 of 7

Math Help - Working with vectors

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Working with vectors

    I know how to compute scalar and cross products but I'm not very familiar with what other rules applies to vectors.

    For example If I have the vectors u and v and the following equation u x (u+v) - v x (3u+v) and I know that u x v = {3,1,-1}
    how do they arrive at 4uxv when simplifying the equation? Also in what order should you do the calculations, does cross product come before dot and addition/subtraction?
    Last edited by dipsy34; July 27th 2012 at 07:21 AM. Reason: misstyped problem
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,677
    Thanks
    1618
    Awards
    1

    Re: Working with vectors

    Quote Originally Posted by dipsy34 View Post
    I know how to compute scalar and cross products but I'm not very familiar with what other rules applies to vectors. For example If I have the vectors u and v and the following equation u x v(u+v) - v(3u+v) and I know that u x v = {3,1,-1}
    how do they arrive at 4uxv when simplifying the equation? Also in what order should you do the calculations, does cross product come before dot and addition/subtraction?
    It appears that part of your confusion may be use of notation. For example v(3u+v) has no real meaning.
    If it were v\times (3u+v) then fine. That equals 3(v\times u)+(v\times v)=3(v\times u) because (v\times v)=0~.

    Do you understand u\times v is a vector, while u\cdot v is a scalar.
    Thus (u\cdot v)\times w is meaningless. Whereas u\times(v\times w)=(u\cdot w)v-(u\cdot v)w.

    You can repost your question with corrections.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Re: Working with vectors

    Fixed the problem to the correct one.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,677
    Thanks
    1618
    Awards
    1

    Re: Working with vectors

    Quote Originally Posted by dipsy34 View Post
    I know how to compute scalar and cross products but I'm not very familiar with what other rules applies to vectors. For example If I have the vectors u and v and the following equation u \times (u+v) - v \times (3u+v) and I know that u \times v = {3,1,-1} how do they arrive at 4uxv when simplifying the equation?
    u \times (u+v)=(u\times u)+(u\times v)=(u\times v) ~ and ~ - v \times (3u+v)=(- v \times 3u)=3(u\times v)
    Recall that - v \times u= u\times v~.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: Working with vectors

    when using latex, use \times for the "x" symbol, instead of the letter x, which displays differently.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Re: Working with vectors

    Quote Originally Posted by Plato View Post
    ~ - v \times (3u+v)=(- v \times 3u)
    This is the part I'm struggling with atm, the others I follow, what are the rules for crossing in the -v in to the parenthesis?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: Working with vectors

    the cross-product distributes over addition, so

    a x (b + c) = (a x b) + (a x c).

    here, your "a" is -v, the "b" is 3u, and the "c" is v, so we have:

    -v x (3u + v) = (-v x 3u) + (-v x v)

    the cross-product is also compatible with scalar multiplication:

    (ra) x b = a x (rb) = r(a x b).

    in particular, for r = -1, and a = b = v:

    -v x v = (-1)v x v = (-1)(v x v) = (-1)(0) = 0.

    thus

    (-v x 3u) + (-v x v) = (-v x 3u) + 0 = -v x 3u
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 05:10 PM
  2. Replies: 3
    Last Post: June 30th 2011, 08:05 PM
  3. Replies: 2
    Last Post: June 18th 2011, 10:31 AM
  4. Working with gradient vectors
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 11th 2011, 09:50 PM
  5. Replies: 4
    Last Post: May 10th 2009, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum