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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.6.3 .
Let
\(P_0 = (1,2,-1)\text{,}\) \(P_1 = (1, 0 ,-1)\text{,}\) and
\(P_2 = (0,1,3)\) and let
\(p\) be the plane containing
\(P_0\text{,}\) \(P_1\text{,}\) and
\(P_2\text{.}\)
(a) Determine the components of the vectors
\(\overrightarrow{P_0P_1}\) and
\(\overrightarrow{P_0P_2}\text{.}\)
(b) Find a normal vector
\(\vn\) to
\(p\text{.}\)
(c) Find a scalar equation of
\(p\text{.}\)
(d) Consider a second plane
\(q\) with scalar equation
\(-3(x-1) + 4(y+3) + 2(z-5)=0\text{.}\) Find two different points on
\(q\) as well as a vector
\(\vm\) that is normal to
\(q\text{.}\)
(e) What is the angle between planes
\(p\) and
\(q\text{?}\)
