Results 1 to 8 of 8

Math Help - Quick elementary question regading vectors

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    48

    Quick elementary question regarding vectors

    The below picture is actually a top-down view of a 3d cube. The corners on the cube are labelled points A, B, C, and D.



    My question is: If I know that the vector AC = (-11, 26, 8) and BD = (-26, 11, 0), how can I find the 3d coordinates for point D? In other words: B = (x, y, 0), find x and y.

    I know it involves halfing both vectors to obtain the midpoint of CA and BD, just not sure how to use that information to find x and y.

    EDIT: If helpful, point C = (2, 4, 17).
    Last edited by Ares_D1; August 8th 2009 at 08:55 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    Remember the magnitude (length) of a vector is:

     l = \sqrt{x_1^2 + x_2^2 + ... + x_n^2}

    Where x_1^2 + x_2^2 + ... + x_n^2 are the number of coordinates you have.

    In this case we have 3. So the length or AC = \sqrt{x^2 + y^2 + z^2}

    By the way, did you come up with C = (2, 4 , 17) on your own? Or was that a given? Also, is it specific where the points are on the cube? From that picture they all look to be on the same side, but that might not be true.
    Last edited by eXist; August 8th 2009 at 09:32 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2009
    Posts
    48
    Quote Originally Posted by eXist View Post
    Remember the magnitude (length) of a vector is:

     l = \sqrt{x_1^2 + x_2^2 + ... + x_n^2}

    Where x_1^2 + x_2^2 + ... + x_n^2 are the number of coordinates you have.

    In this case we have 3. So the length or AC = \sqrt{x^2 + y^2 + z^2}

    By the way, did you come up with C = (2, 4 , 17) on your own? Or was that a given? Also, is it specific where the points are on the cube? From that picture they all look to be on the same side, but that might not be true.
    Point C was given.

    Yes I'm aware of the length formula, but I don't think that is helpful for finding the coordinates of D.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    To me, it seems like there are 2 answers because you are un-aware of whether C and D like on the same side or not. You can find the dimensions of the cube fairly easy by finding the length of   BD = \sqrt{(-26)^2 + (11)^2} = \sqrt{797} this gives you the length of the diagonal of one side.

    Since the triangle that is made by dividing the side of a cube by a diagonal is a 45/45/90 triangle, we know that the length of cube = \sqrt{797}/\sqrt{2} = \sqrt{797/2}

    Now that we have the length of a side, we don't know whether D lies above or below C.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2009
    Posts
    48
    Quote Originally Posted by eXist View Post
    To me, it seems like there are 2 answers because you are un-aware of whether C and D like on the same side or not. You can find the dimensions of the cube fairly easy by finding the length of  BD = \sqrt{(-26)^2 + (11)^2} = \sqrt{797} this gives you the length of the diagonal of one side.

    Since the triangle that is made by dividing the side of a cube by a diagonal is a 45/45/90 triangle, we know that the length of cube = \sqrt{797}/\sqrt{2} = \sqrt{797/2}

    Now that we have the length of a side, we don't know whether D lies above or below C.
    D lies below C, it is given in the problem.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    Quote Originally Posted by Ares_D1 View Post
    D lies below C, it is given in the problem.
    This helps, but our work isn't done. We need to find some more points on the cube. How can we find A with the info that we have?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Apr 2009
    Posts
    48
    Quote Originally Posted by eXist View Post
    This helps, but our work isn't done. We need to find some more points on the cube. How can we find A with the info that we have?
    A is given too lol. Sorry, didn't realize we would need it.

    A = (13, 30, 9) (I've rounded the coordinates for simplicity, shouldn't matter for now, just trying to figure out the method rather than the actual answer).
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    Well now that we know 2 corners of the cube, this determines the cube. Therefore we can find the other points.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 21st 2009, 01:31 PM
  2. Quick Vectors Question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 12th 2009, 06:25 AM
  3. Quick Easy Vectors Question
    Posted in the Math Topics Forum
    Replies: 7
    Last Post: May 21st 2009, 09:19 PM
  4. Elementary Challenge Question
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 4th 2008, 04:24 PM
  5. Elementary Set Question
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: September 11th 2008, 02:05 AM

Search Tags


/mathhelpforum @mathhelpforum