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?