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Finding orthogonal unit vector to a plane

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




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)

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?
 

Charles Link

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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.
 

Ray Vickson

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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




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)

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?
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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