Find a unit vector that is orthogonal to the plane

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?

Find a unit vector that is orthogonal to the plane by Linear Transformation

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Originally Posted by

**nemixus** 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?

*Can the desired vector be generated by linear transformation?*