First slide
Introduction to Determinants
Question

If three distinct points P3u2,2u3;Q3v2,2v3 and R3w2,2w3 are collinear, then uv + vw + wu is equal to

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Solution

3u22u313v22v313w22w31=0 R1R1R2 and R2R2R3 or  u2v2u3v30v2w2v3w30w2w31=0

 or u+vu2+v2+vu0v+wv2+w2+vw0w2w31=0R1R1R2 or uwu2w2+v(uw)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)2u(v+w)=0or uv+vw+wu=0

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