Answer :

Given :


A = (2, -1, 1)


Direction ratios of perpendicular vector = (4, 2, -3)


To Find : Equation of a 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 the equation of a plane is



Where,




For point A = (2, -1, 1), position vector is



Vector perpendicular to the plane with direction ratios (4, 2, -3) is



Now,


= 8 – 2 – 3


= 3


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




As



= 4x + 2y – 3z


Therefore, the equation of the plane is


4x + 2y – 3z = 3


Or


4x + 2y – 3z - 3 = 0


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