Vectors in plane question

Question

let P be the plane x+y+z=0. show that any linear combination of v₁=(1,-1,0) and v₂=(0,1,-1) is in P.

Answer 1

Origin (0, 0, 0) on this plane (0 + 0+ 0 = 0). v₁ also on plane because (1 - 1+ 0 = 0) and v₂ also (0 + 1 - 1 = 0)