Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector $3\hat i + 5\hat j - 6\hat k.$

. : Let $\vec n = 3\hat i + 5\hat j - 6\hat k$

Then,$|\vec n| = \sqrt {9 + 25 + 36} = \sqrt {70} \Rightarrow \hat n = \cfrac{{\vec n}}{{|\vec n|}} = \cfrac{1}{{\sqrt {70} }}(3\hat i + 5\hat j - 6\hat k)$

Hence, the required equation of the plane is