How to find a vector perpendicular to plane ABC given A,B and C

Question

Let $A=(1,0,1)$, $B=(2,1,-1)$, $C(0,1,2)$

Find a vector perpendicular to the plane $ABC$.

the solution I was given by my lecturer:

Does it matter which vectors I use?

Because my attempt has got the exact opposite sign.

Answer 1

Your attempt is basically alright.

Take combination ABC and compute a unit normal vector P . Next take combination DBC and compute a unit normal vector Q.

In general, cross product M X N has sign opposite to that of N X M. The product vectors have opposite sense.

If P,Q are same then the sense is same, else the opposite sense has prevailed.

(If the vectors are altogether different then the four sides are not in the same plane.)