If three distinct points P3u2,2u3;Q3v2,2v3 and R3w2,2w3 are collinear, then uv + vw + wu is equal to
3u22u313v22v313w22w31=0 R1→R1−R2 and R2→R2−R3 or u2−v2u3−v30v2−w2v3−w30w2w31=0
or u+vu2+v2+vu0v+wv2+w2+vw0w2w31=0R1→R1−R2 or u−wu2−w2+v(u−w)0v+wv2+w2+vw0w2w31=0
or 1u+w+v0v+wv2+w2+vw0w2w31=0or v2+w2+vw−(v+w)[(v+w)+u]=0or v2+w2+vw−(v+w)2−u(v+w)=0or uv+vw+wu=0