Q. 19

Write the equation of the plane passing through the point (a, b, c) and parallel to the plane

Answer :

Given :


A ≡ (a, b, c)


Equation of plane parallel to required plane



To Find : Equation of plane


Formulae :


1) Position vectors :


If A is a point having co-ordinates (a1, a2, a3), then its position vector is given by,



2) Dot Product :


If are two vectors




then,



3) Equation of plane :


If a plane is passing through point A, then equation of plane is



Where,




Answer :


For point A ≡ (a, b, c), position vector is



As plane is parallel to the required plane, the vector normal to required plane is



Now,


= a + b + c


Equation of the plane passing through point A and perpendicular to vector is




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