Find the equation of the plane passing through the points
(0,1,0) (1,0,2) and (2,1,3)

Answer 
Let P(0,1,0) Q(1,0,2) and R(2,1,3)
PQ = <1, -1, 2>
PR = <2, 0, 3>
    | i  j  k |
n = | 1 -1  2 | = <|-1 2|, - |1 2|, |1 -1|> = <-3, 1, 2>
    | 2  0  3 |    | 0 3|    |2 3|  |2  0|

check
<-3, 1, 2> dot <1, -1, 2> = -3 -1 + 4 = 0 check
<-3, 1, 2> dot <2, 0, 3> = -6 +0 + 6 = 0 check

-3 x + y + 2 z = -3(0) + 1(1) + 2(0) = 1
-3 x + y + 2 z = 1