Q. 55.0( 4 Votes )

Find the vector, and Cartesian equations of a plane which passes through the point (1, 4, 6) and the normal vector to the plane is

Answer :

Given :


A = (1, 4, 6)



To Find : Equation of plane.


Formulae :


1) Position Vector :


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 :


Equation of plane passing through point A and having as a unit vector normal to it is



Where,


Position vector of point A = (1, 4, 6) is



Now,



= (1×1) + (4×(-2)) + (6×1)


= 1 – 8 + 6


= - 1


Equation of plane is




This is vector equation of the plane.


As


Therefore



= (x × 1) + (y × (-2)) + (z × 1)


= x - 2y + z


Therefore equation of the plane is



This is Cartesian equation of the plane.


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