Answer :

Given :


P = (1, 2, -3)


O = (0, 0, 0)



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) Vector :


If A and B be two points with position vectors respectively, where




then,




3) Dot Product :


If are two vectors




then,



4) Equation of plane :


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



Where,




For points,


P = (1, 2, -3)


O = (0, 0, 0)


Position vectors are




Vector





Now,



= 1 + 4 + 9


= 14


And



= x + 2y + 3z


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



But,


Therefore, the equation of the plane is



x + 2y + 3z = 14


x + 2y + 3z – 14 = 0


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