How would you show that a vector is normal to a plane in 3D space?
There are 2 main methods for finding a normal vector.
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If you know two vectors that lie in the plane e.g. (a,b,c) and (d,e,f), we can find a normal vector by calculating the vector/cross product of (a,b,c) and (d,e,f). This works because the vector product produces a new vector perpendicular to both your starting vectors, so it must be at right angles to the plane.
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If on the other hand you know the Cartesian equation of a plane, which looks like (ax)+(by)+(cz)=0, then the vector (a,b,c) is a normal vector!
