How to find a unit vector that is normal (perpendicular) to a plane determined by three points?

Find a unit vector that is normal (perpendicular) to the plane determined by the points A(1, - 1, 2)


,B(2,0, - 1) and C(0,2,1).





I have no idea whatsoever about how to solve this one. All help is really appreciated!|||Form two vectors with your points. e.g.





AB = (1, 1, -3) and AC = (-1, 3, -1).





The cross product of these will be normal to the plane. To get a unit normal, just divide the cross product by its magnitude.





v = AB x AC = (8, 4, 4).





||v|| = 鈭?8虏 + 4虏 + 4虏) = 4鈭?6).





n = v/||v|| = (2/鈭?6), 1/鈭?6), 1/鈭?6)).