Activity 9.7.2

Write a scalar equation of the plane $p_1$ passing through the point $(0, 2, 4)$ and perpendicular to the vector $\vn=\langle 2, -1, 1\rangle$.

Is the point $(2, 0, 2)$ on the plane $p_1$?

Write a scalar equation of the plane $p_2$ that is parallel to $p_1$ and passes through the point $(3, 0, 4)$.

Give parametric equations for the line $\mathcal{L}$ passing through the point $(2,0,2)$ and perpendicular to the plane $p_3$ described by the equation $x+2y-2z = 7$.

Find the point at which $\mathcal{L}$ intersects $p_3$.