# Find the Vector Equation of the Plane Passing Through a Point Having Position Vector 3i-2j+k and Perpendicular to the Vector 4i+3j+2k - Mathematics and Statistics

Find the vector equation of the plane passing through a point having position vector 3 hat i- 2 hat j + hat k and perpendicular to the vector 4 hat i + 3 hat j + 2 hat k

#### Solution

We know that the vector equation of a plane passing through a point  A(bara) and normal to bar r .bar n=bar a.barn
Here  bar a =3hati- 2hat j + hat k and hatn = 4hati +3 hatj+2hatk

The vector equation of the required plane is

bar r .bar n=bar a.barn

bar r.(4hati+3hatj+2hatk)=(3hati-2hatj+hatk).(4hati+3hatj+2hatk)

bar r.(4hati+3hatj+2hatk)=12-6+2

bar r.(4hati+3hatj+2hatk)=8

The vector equation of the required plane is  bar r.(4hati+3hatj+2hatk)=8

Concept: Vector and Cartesian Equation of a Plane
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