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Math Help - two unit vectors orthogonal

  1. #1
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    two unit vectors orthogonal

    find two unit vectors orthogonal to both

    <1, -1, 1> and <0, 4, 4>

    can ya run down through this problem please.

    there were square roots in the answer, i thought this was just dot product?

    thanks.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    find two unit vectors orthogonal to both

    <1, -1, 1> and <0, 4, 4>

    can ya run down through this problem please.

    there were square roots in the answer, i thought this was just dot product?

    thanks.
    o_O showed you how to do the cross product.

    (1,-1,1) \times (0,4,4) = (-8,-4,4)

    Now calculate the absolute value of the resulting vector:

    |(-8,-4,4)| = \sqrt{96}=4\sqrt{6}

    Divide the result by the absolute value to reduce the vector to the length 1:

    \overrightarrow{u_1} = \dfrac{(-8,-4,4)}{4\sqrt{6}} = (-2\sqrt{6}, -\sqrt{6}, \sqrt{6})

    \overrightarrow{u_2} = \dfrac{(-8,-4,4)}{-4\sqrt{6}} = (2\sqrt{6}, \sqrt{6}, -\sqrt{6})
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  3. #3
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    thanks, ya was cross product not dot product.

    used (-4 -4) - (4-0) + (4-0)

    for -8, -4. 4

    thankyou, especially for the breakdown on the rest of the problem.
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