Find the vector equation of a plane passing through a point having position vector and perpendicular to the vector

Given: Position vector of the point -

Point is perpendicular to the vector

To find: the vector equation of a plane passing through a point

We know that, vector equation of a plane passing through a point and normal to is given by

Substituting the values from given criteria, we get

(by multiplying the two vectors using the formula )

is the vector equation of a plane passing through the given point.