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Math Help - Linear independent vectors perpendicular to vector v.

  1. #1
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    Linear independent vectors perpendicular to vector v.

    Find 2 linear independent vectors perpendicular to the vector v=[1,-1,5]^T.


    I tried doing cross product and then plugging in random numbers to find solve this equal to 0. I then came up with 2 different vectors with but it is not correct.

    Please Help?

    thank you,
    diggidy
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  2. #2
    MHF Contributor

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    Doing cross product of what two vectors? You are only given one vector. Any vector, <x, y, z>, perpendicular to <1, -1, 5> must satisfy x- y+ 5z= 0 (their dot product is 0). Solve that for x: x= y- 5z.

    So <x, y, z>= <y- 5z, y, z>= <y, y, 0>+ <-5z, 0, z>= y<1, 1, 0>+ z<-5, 0, 1>.

    Now, what are two vectors that are perpendicular to <1, -1, 5>? Are they independent?
    Last edited by HallsofIvy; April 7th 2011 at 08:48 AM.
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