IB Mathematics Analysis and Approaches 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 $\mathbf{n}=\left(\begin{array}{c}2\\ 1\\ -1\end{array}\right)$ passing through the point $A(1,2,3)$.

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

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

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

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

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

Find the scalar equation of the plane with normal vector $\mathbf{n}=\left(\begin{array}{c}0\\ 1\\ -2\end{array}\right)$ 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 $A(4,5,1)$.