Answer :

Given :


A = (1, 2, 3)


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


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 = (1, 2, 3), position vector is



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



Now,


= 2 + 6 – 12


= - 4


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




As



= 2x + 3y – 4z


Therefore, equation of the plane is


2x + 3y – 4z = -4


Or


2x + 3y – 4z + 4 = 0


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