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**1. Homework Statement**

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

x − y + √2z=5

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. Homework Equations**

**3. The Attempt at a Solution**

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

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?