Q. 6

Find the length of the perpendicular from the origin to the plane Also write the unit normal vector from the origin to the plane.

Answer :

Given :


Equation of plane :


To Find :


i) Length of perpendicular = d


ii) Unit normal vector =


Formulae :


1) Unit Vector :


Let be any vector


Then unit vector of is



Where,


2) Length of perpendicular :


The length of the perpendicular from the origin to the plane


is given by,



Given the equation of the plane is





Comparing the above equation with



We get,


& p = 39


Therefore,





= 13


The length of the perpendicular from the origin to the given plane is





Vector normal to the plane is



Therefore, the unit vector normal to the plane is





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