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

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

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

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

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

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

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

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

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

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

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