Show that the points (−2,3,5),(1,2,3) and (7,0,−1) are collinear.
Let points (−2,3,5),(1,2,3) and (7,0,−1) be denoted by P,Q and R respectively.Points
P,Q and
R are collinear if they lie on a line.
PQ=√(1+2)2+(2−3)2+(3−5)2=√(3)2+(−1)2+(−2)2=√9+1+4=√14QR=√(7−1)2+(0−2)2+(−1−3)2=√(6)2+(−2)2+(−4)2=√36+4+16=√56=2√14PR=√(7+2)2+(0−3)2+(−1−5)2=√(9)2+(−3)2+(−6)2=√81+9+36=√126=3√14
Here PQ+QR=√14+2√14
=3√14
=PR
⇒PQ+QR=PR
Hence points P(−2,3,5),Q(1,2,3) and R(7,0,−1) are collinear