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Math Help - Vectors: Find the length and direction of u * v

  1. #1
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    Vectors: Find the length and direction of u * v

    Sorry I meant x not *
    I need to find the length and direction of u x v, and I have:
    u = i x j
    v = j x k
    So first I will find:

    <br />
u \times v = <br />
\left[ {\begin{array}{ccc}<br />
 i & j & k  \\<br />
1 & 1 & 0  \\<br />
0 & 1 & 1 \end{array} } \right] <br />
= i - j + k<br />

    Then the length is 1 and direction is i - j + k.
    Am I doing this correctly?
    Last edited by tintin2006; November 15th 2010 at 06:34 PM. Reason: For clarification
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  2. #2
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    Quote Originally Posted by tintin2006 View Post
    I need to find the length and direction of u * v, and I have:
    u = i * j
    v = j * k
    So first I will find:

    <br />
u * v = <br />
\left[ {\begin{array}{ccc}<br />
 i & j & k  \\<br />
1 & 1 & 0  \\<br />
0 & 1 & 1 \end{array} } \right] <br />
= i - j + k<br />

    Then the length is 1 and direction is i - j + k.
    Am I doing this correctly?
    I assume you mean * to indicate the cross product of two vectors

    u = i \times j = k<br />

    v = j \times k = i

    so ...

    u \times v = k \times i = j
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  3. #3
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    Quote Originally Posted by tintin2006 View Post
    I need to find the length and direction of u * v, and I have:
    u = i x j
    v = j x k
    So first I will find:

    <br />
u x v = <br />
\left[ {\begin{array}{ccc}<br />
 i & j & k  \\<br />
1 & 1 & 0  \\<br />
0 & 1 & 1 \end{array} } \right] <br />
= i - j + k<br />
    For " \times" use "\times" not "x".

    Then the length is 1 and direction is i - j + k.
    Am I doing this correctly?
    I find it difficult to understand what you are asking. You used "*" at one point and \times at another. Are they both intended to be the cross product? Also, you say that u= i x j= k and v= j x k= i but then you have i+ j and j+ k instead. Yes, (i+ j)\times(j+ k)= i- j+ k but that has length \sqrt{1^2+ (-1)^2+ 1^2}= \sqrt{3}, not 1.
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  4. #4
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    Sorry and thanks for the tip.
    I meant cross product, I didn't notice that * could mean dot product
    Why does skeeter's solution is so different from mine? Are they the same thing?
    u = i \times j = k<br />

    v = j \times k = i

    so ...
    u \times v = k \times i = j
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