Results 1 to 5 of 5

Math Help - Find vectors

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Find vectors

    Find 4 vectors  V_{1},V_{2},V_{3},V_{4} such that |V_{i}| = 1 \ for \ i=1,2,3,4, (V_{i},V_{j})=0, i \neq j
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,805
    Thanks
    696
    Hello, tttcomrader!

    I don't understand the problem . . .


    Find 4 vectors:  V_{1},V_{2},V_{3},V_{4}\text{ such that }|V_{i}| = 1\text{ for }i=1,2,3,4 . . . . They are unit vectors

    and: . (V_{i},V_{j})=0,\;i \neq j .
    . . . What does this mean?

    If you meant: . V_i\cdot V_j \:=\:0, we have four mutually perpendicular vectors.

    This is possible in dimensions greater than or equal to 4.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2
    I asked the professor and I finally understand what he was writing, the correct question is:

    Find 4 vectors  V_{1},V_{2},V_{3},V_{4} such that |V_{i}| = 1 \ for \ i=1,2,3,4, (V_{i}V_{j})=e, i \neq j

    He also gave me a hint:

    Consider the unite cube and the regular tetrahedron which vertices are among the vertices of the cube. Connect the center of the cube with the vertices of the tetrahedron.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,805
    Thanks
    696
    Hello, tttcomrader!

    It still has unanswered questions . . .


    Find 4 vectors  V_1,\:V_2,\:V_3,\:V_4 such that: . |V{i}| = 1 for i=1,2,3,4 .(unit vectors)

    and: . (V_iV_j)\:=\:e,\;\;i \neq j. . I still don't know what {\color{blue}(V_iV_j)} means ... dot product?

    And does it really equal e = 2.71828... ?


    He also gave me a hint:
    Consider the unit cube and the regular tetrahedron which vertices are
    among the vertices of the cube. Connect the center of the cube with
    the vertices of the tetrahedron. . Then what?

    Place the cube in the first octant with one vertex at the origin.

    The vertices are: . A(0,0,0),\;B(1,1,0),\;C(0,1,1),\;D(1,0,1),\;\;(1,0  ,0),\;(0,1,0),\;(0,0,1),\;(1,1,1)

    A,\,B,\,C,\,D are the vertices of a regular tetrahedron with side \sqrt{2}.

    The center of the cube is: . O\left(\frac{1}{2},\:\frac{1}{2},\:\frac{1}{2}\rig  ht)


    Then: . \begin{array}{ccccc}V_1 &=& OA &=& \langle \text{-}\frac{1}{2},\;\text{-}\frac{1}{2},\:\text{-}\frac{1}{2}\rangle \\<br />
V_2 &=& OB&=&\langle \frac{1}{2},\:\frac{1}{2},\:\text{-}\frac{1}{2}\rangle \\<br />
V_3 &=&OC &=&\langle\text{-}\frac{1}{2},\:\frac{1}{2},\:\frac{1}{2}\rangle \\<br />
V_4 &=& OD &=& \langle \frac{1}{2},\:\text{-}\frac{1}{2},\:\frac{1}{2}\rangle\end{array} . . (These are not unit vectors.)


    Is there an original wording of the problem?

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2
    It is dot product.  e_{1} = (1,0,0)

    I asked him how to do this, he explained to me a great deal, but I do not get any of it, as a matter of fact, I still don't understand what the question is asking. I don't think I'm a stupid person, after all I did finish my history BA and math BS with GPA over 3.6, but in this class, I"m completely lost no matter how hard I try...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vectors, find N(1)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 13th 2011, 04:14 AM
  2. Find vectors T, N, and B at the given point
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 17th 2009, 07:46 PM
  3. vectors, find v, a, s
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 8th 2009, 08:51 PM
  4. Given vectors find the matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 13th 2009, 09:41 AM
  5. Find vectors b1 and b2
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 9th 2009, 12:44 AM

Search Tags


/mathhelpforum @mathhelpforum