Question Type 3: Finding equation of a plane given the normal and a point Bootcamps

Find the scalar equation of the plane with normal vector $\mathbf{n} = (0,1,-2)$ passing through the point $A(3,4,5)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (1,1,1)$ passing through the point $A(1,0,2)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (2,3,1)$ passing through the point $A(4,5,1)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (1,-2,3)$ passing through the point $A(2,0,-1)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (-4,3,0)$ passing through the point $A(0,2,1)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (3,-3,6)$ passing through the point $A(2,5,-4)$.

Find the vector equation of the plane with normal vector $\mathbf{n} = (2,1,-1)$ passing through the point $A(1,2,3)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (5,2,-3)$ passing through the point $A(1,-1,2)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = (7,0,-5)$ passing through the point $A(3,-2,4)$.

Find the vector equation of the plane with normal vector $\mathbf{n} = (0,4,5)$ passing through the point $A(-1,0,2)$.

Find the vector equation of the plane with normal vector $\mathbf{n} = (6,-2,3)$ passing through the point $A(4,4,4)$.

Find the scalar equation of the plane with normal vector $\mathbf{n} = \bigl(\tfrac12,\tfrac23,-\tfrac13\bigr)$ passing through the point $A(3,1,-2)$.