Q. 265.0( 1 Vote )

Write the equatio

Answer :

Given :


A ≡ (2, -1, 1)


Plane parallel to the required plane : 3x + 2y – z = 7


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 ≡ (2, -1, 1), position vector is



As required plane is parallel to 3x + 2y – z = 7.


Therefore, normal vector of given plane is also perpendicular to required plane



Now,


= 6 – 2 – 1


= 3


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




As



= 3x + 2y – z


Therefore, equation of the plane is


3x + 2y – z = 3


3x + 2y – z - 3 = 0


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