Question

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

Answer 1

We know that the vector equation of the plane passing through `A(bara)` and normal to vector `barn` is given by `barr * barn = bara * barn`.

Here `bara = 2hati + 3hatj + 4hatk, barn = 2hati + hatj - 2hatk`

`bara * barn = (2hati + 3hatj + 4hatk) * (2hati + hatj - 2hatk)`

= 4 + 3 − 8

= −1

The vector equation of the plane is `barr*(2hati + hatj - 2hatk)` = −1