The normal vector to all of these vectors will have the same equation as the plane that contains all three vectors.
Find all vectors N that are orthogonal to a b and c where
a =[1 2 3 4]; b =[-1 2 -3 -4]; c =[2 4 6 10]
my idea is, since the dot product between to vectors is 0, we could do the same thing for all the vectors such that
n*a = 0
n*b = 0
n*c = 0
and then implement them into a system of linear equations such that
n_1 + 2n_2 + 3n_3 +4n_4 = 0
-n_1 + 2n_2 - 3n_3 - 4n_4 = 0
2n_1 + 4n_2 + 6n_3 + 10n_4 = 0
where n_(1-4) are all the variables of the vector N such that
N = [n_1 n_2 n_3 n_4]
would this be a valid way to approach this?