# Finding orthogonal unit vector to a plane

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1. Nov 7, 2016

### Erenjaeger

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. Nov 7, 2016