Which of the following is a vector space under standard operations on R3\mathbb{R}^3R3?
V={(x,y,z):x2+y2+z2=1}V = \{(x, y, z) : x^2 + y^2 + z^2 = 1\}V={(x,y,z):x2+y2+z2=1} (unit sphere)
V={(x,y,z):x+y−2z=0}V = \{(x, y, z) : x + y - 2z = 0\}V={(x,y,z):x+y−2z=0} (plane through origin)
V={(x,y,z):x,y,z≥0}V = \{(x, y, z) : x, y, z \geq 0\}V={(x,y,z):x,y,z≥0} (first octant)
V={(x,y,z):xy+z=1}V = \{(x, y, z) : xy + z = 1\}V={(x,y,z):xy+z=1}