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Simple Hyperplane Equation - What am I Missing?

  1. Jul 13, 2011 #1
    I'm trying to learn linear algebra using Schaum's outline and this is one of the practice problems:

    Find and equation of the hyperplane H in R4 that passes through P(3,-4,1,-2) and is normal to u=[2,5,-6,-3]

    The equation is in the form 2x1+5x2-6x3-3x4 = k

    They say to substitute P into the equation to obtain k=-26 but I keep coming up with k=-14. This is simple math but I'm clearly missing something. Where am I going wrong?
     
  2. jcsd
  3. Jul 13, 2011 #2

    micromass

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    It's probably a typo.
     
  4. Jul 13, 2011 #3
    Let X be a point in the hyperplane. Then u.(X-P)=0 should be your equation.

    So, 2(x1 - 3) + 5(x2 + 4) - 6(x3 - 1) - 3(x4 + 2) = 0

    2x1 + 5x2 - 6x3 - 3x4 + 14 = 0

    Same answer you get. Is there a typo somewhere?
     
  5. Jul 13, 2011 #4
    There has to be a typo because the next problem is similar and the answer there is correct.
     
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