Q. 8

Find the vector equation of a plane whose Cartesian equation is 5x - 7y + 2z + 4 = 0.

Answer :

Given :


Cartesian equation of the plane is


5x – 7y + 2z + 4 = 0


To Find : Vector equation of the given plane.


Formulae :


1) Dot Product :


If are two vectors




then,



Given the equation of the plane is


5x – 7y + 2z + 4 = 0


5x – 7y + 2z = - 4


The term (5x – 7y + 2z) can be written as



But



Therefore the equation of the plane is



or



This is Vector equation of the given plane.


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