Question

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`

 

Answer 1

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`