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Homework Help: Finding orthogonal unit vector to a plane

  1. Nov 7, 2016 #1
    1. The problem statement, all variables and given/known data

    find the vector in R3 that is a unit vector that is normal to the plane with the general equation

    x − y + √2z=5

    2. Relevant equations

    3. The attempt at a solution

    so the orthogonal vector, I just took the coefficients of the general equation, giving (1, -1, √2)

    then because it says unit vector i used the fact that v/||v|| gives the unit vector of 'v'
    solving for the unit vector (1/2, -1/2, √2/2)
    but the correct answer is (-1/2, 1/2, -1,√2)
    where have i gone wrong?
  2. jcsd
  3. Nov 7, 2016 #2

    Charles Link

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    Gold Member

    Is your vector a unit vector? (amplitude=1). You need to normalize it. It is equally correct if it points in the opposite direction. editing... Reading it closer I see you correctly normalized it. @Ray Vickson also answers it correctly in the post that follows.
  4. Nov 7, 2016 #3

    Ray Vickson

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    Both versions are correct: they are both unit vectors, and both of them are perpendicular to the plane. They just point in opposite directions: one points North and the other points South.
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