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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.6.2 .
(a) Write a scalar equation of the plane
\(p_1\) passing through the point
\((0, 2, 4)\) and perpendicular to the vector
\(\vn=\langle 2, -1, 1\rangle\text{.}\)
(b) Is the point
\((2, 0, 2)\) on the plane
\(p_1\text{?}\)
(c) Write a scalar equation of the plane
\(p_2\) that is parallel to
\(p_1\) and passes through the point
\((3, 0, 4)\text{.}\)
Hint .
Compare normal vectors of the planes.
(d) 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
\(x+2y-2z = 7\text{.}\)
(e) Find the point at which
\(\mathcal{L}\) intersects
\(p_3\text{.}\)
