Find the vector equation of the plane passing through a point having position vector `3hati - 2hatj + 3hatk` and perpendicular to the vector `4hati + 3hatj + 2hatk`.

Explanation

Let `bara = 3hati - 2hatj + hatk` and `barn = 4hati + 3hatj + 2hatk.`
The vector equation of the plane passing through the point A`(bara)` and perpendicular to the vector `barn` is `barr*barn = bara*barn`.
Here, `bara*barn = (3hati - 2hatj + hatk) * (4hati + 3hatj + 2hatk)`
` = 3(4) + (-2)(3) + 1(2)`
` = 12 - 6 + 2 = 8`
`therefore` the vector equation of the required plane is `barr* (4hati + 3hatj + 2hatk) = 8`.