Class 12

Math

3D Geometry

Three Dimensional Geometry

Show that the points $A(2,3,4),B(−1,−2,1)$ and $C(5,8,7)$ are collinear.

D.r's of $AB$ are $(3+2),(−6−4),(−8−7)$ ie., $5,−10,−15$ ie., $1,−2,−3$

Dr's of $AC$ are $(1+2),(−2−4),(−2−7)$ ie., $3,−6,−9$ ie., $1,−2,−3$

$AB∥AC$ and both have a common end point $A$

Hence $A,B,C$ are collinear