I was given a vector A = [2 2 2] and a vector B = [4 6 5] from a plane and supposed to find a vector orthogonal to this plane. The vector has to intersect with the plane at [0 0 0]and have length 1. I was given a hint that the dot product of these two vectors with the orthogonal vector should be zero. How do I do that?

Also, can the desired vector be generated by linear transformation?