Results 1 to 5 of 5

Math Help - Help with Calculating the Cross and Dot Product

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Atlanta
    Posts
    3

    Help with Calculating the Cross and Dot Product

    I have figured out how to determine the Dot product becasue it is fairly straight forward. However the Cross product seems to be a challenge for me as I cannot seem to grasp.

    Here is the Problem

    Determine: AXB if A = 3i - 2j and B = i + 2k

    Need help working out this problem......
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member kalyanram's Avatar
    Joined
    Jun 2008
    From
    Bangalore, India
    Posts
    142
    Thanks
    14

    Re: Help with Calculating the Cross and Dot Product

    Consider A = u+v, B=x+y where u=3i, v=-2j, x=i \hspace{2mm}and \hspace{2mm}y=2k.
    Spoiler:

    Now Ax B = (u+v)x (x+y) = ux (x+y)+vx (x+y)(why?)
    \implies ux x+ ux y + vx x+ vx y(why?)
    Now substitute their respective values and simplify.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: Help with Calculating the Cross and Dot Product

    Quote Originally Posted by biglew404 View Post
    I have figured out how to determine the Dot product becasue it is fairly straight forward. However the Cross product seems to be a challenge for me as I cannot seem to grasp.
    Here is the Problem
    Determine: AXB if A = 3i - 2j and B = i + 2k
    Evaluate the determinate by expanding alone the first row:
    A\times B=\left| {\begin{array}{*{20}{c}}  i&j&k \\   3&{ - 2}&0 \\   1&0&2 \end{array}} \right|=~?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,326
    Thanks
    1298

    Re: Help with Calculating the Cross and Dot Product

    That is equivalent to the basic definition of x=cross product:
    i\times j= k, j\times k= i, k\times i= j.
    cross product distributes over addition, and cross product is skew- symmetric ( u\times v= -v\times u).

    So (ai+ bj+ ck)\times (pi+ qj+ rk)= (ai)\times(pi+ qj+ rk)+ (bj)\times(pi+ qj+ rk)+ (ck)\times (pi+ qj+ rk)
    = ap (i\times i)+ aq (i\times j)+ ar(i\times k)+ bp(j\times i)+ bq(j\times j)+ br(j\times k)+ cp(k\times i)+ cq(k\times j)+ cr(k\times k)
    Because cross product is skew symmetric, i\times i= 0, j\times j= 0, k\times k= 0, i\times k= -k\times i= -j, j\times i= -i\times j= -k, and k\times j= -j\times k= -i.

    That reduces the above to [tex](aq- bp)i- (ar- cp)j+ (aq- bp)k which is the same as
    \left|\begin{array}{ccc}i & j & k \\a & b & c \\ p & q & r\end{array}\right|
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2012
    From
    Atlanta
    Posts
    3

    Re: Help with Calculating the Cross and Dot Product

    (-4 - 0)i - (6 - 0)j + (0 - -2)k
    = -4i - 6j + 2K

    Thanks Alot..........I understand better now
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 19th 2011, 10:21 PM
  2. the cross product
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 21st 2010, 09:25 PM
  3. Replies: 4
    Last Post: September 2nd 2009, 04:07 AM
  4. Cross product and dot product relationships
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 15th 2008, 05:45 PM
  5. Replies: 1
    Last Post: May 14th 2008, 11:31 AM

Search Tags


/mathhelpforum @mathhelpforum