if (x,y,z) unequal to (0,0,0) and (i + j + 3k)x + ( 3i - 3j +k)y + (-4i + 5j)z = a(xi + yj + zk), then the value of a is
Attempt: I wrote $$(x+3y-4z) i + (x-3y+5z) j + (3x+y) k = a (x i + y j + z k)$$ Which gave me $$ x+3y-4z=ax\\ x-3y+5z=ay\\ 3x+y=az $$ Now these are 4 unknown and only 3 equations.
Also, i dont know determinant , so please suggest me another way to solve it without using determinants.