Math Is Fun Forum

Could you, please help me with this?

If these two operations are defined as follows. With these new definitions, is R3 a vector space?
a) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 2, y1 + y2 + 2, z1 + z2 + 2)
c(x, y, z)=(cx, cy, cz)

b) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 4, y1 + y2 + 4, z1 + z2 + 4)
c(x, y, z)=(cx + 4c – 4, cy + 4c – 4, cz + 4c – 4)

Thanks!