Question

4. The subset of R3 given by:
V ={(x,y,z)∈R3 |3x+5y+z=0}, with addition and scalar multiplication defined as usual, that is,
(x1,y1,z1)+(x2,y2,z2)=(x1 +x2,y1 +y2,z1 +z2), and λ(x,y,z)=(λx,λy,λz).