Equation of plane passing through points given by position vectors ¯a and ¯b and origin will be
Here we know given the plane passes through points given by position vectors ¯a and ¯b . So the perpendicular to the plane will be along ¯aׯb. Therefore our ^n or unit vector perpendicular to the plane will be ¯aׯb|¯aׯb|. Equation of plane will be
(¯r−0).¯aׯb|¯aׯb|=0.
Which is same as,
¯r.¯aׯb|¯aׯb|=0.