How do you find orthogonal vectors in a plane?

Say for instance you have the plane x + y +2z=0 what would be an orthogonal vectorvector in this plane.



I have another question how do you turn an orthogonal vector to orthonormalHow do you find orthogonal vectors in a plane?Orthogonal vectors: vectors dot product is equal to zero

Som (x i + y j + 2z k) DOT (a i + b j + ck) = o



(ax + yb + 2xc = 0)



Orthonomal = Orthogonal vector / MagnitudeHow do you find orthogonal vectors in a plane?orthagonal to a plane is very easy - you just take the coefficients of the x, y, and z terms. in this case, the orthagonal is %26lt;1, 1, 2%26gt; (1X+1Y+2Z).



orthanormal is simply unit vector of orthagonal. divide by the magnitude, rt6, yielding %26lt;rt6/6, rt6/6, rt(6)/3%26gt;How do you find orthogonal vectors in a plane?orthonormal = orthogonal and has length of 1, so basically divide the vector by it's length (sqrt(6) in your case)