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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.3.2 .
(a) Determine each of the following.
(i)
\(\langle 1, 2, -3 \rangle \cdot \langle 4, -2, 0 \rangle\)
(ii)
\(\langle 0, 3, -2, 1 \rangle \cdot \langle 5, -6, 0, 4 \rangle\)
(b) Let
\(\vu,\vv,\vw\) be vectors in
\(\R^n\text{.}\) Suppose that you know that
\(\vu\cdot \vw = 10\) and
\(\vv\cdot \vw = -3\text{.}\) Compute
\((\vu+\vv)\cdot \vw\text{.}\)
(c) Let
\(\vu,\vv\) be vectors in
\(\R^n\text{.}\) Suppose that you know that
\(\vu\cdot \vv = 3\text{,}\) \(\vecmag{\vu} = 4\text{,}\) and
\(\vecmag{\vv} = 7\text{.}\) Compute
\((\vu+\vv)\cdot (\vu+\vv)\text{.}\)
(d) Let
\(\vu,\vv\) be vectors in
\(\R^n\text{.}\) For what value of
\(t\) is
\((t\vu + \vv) dot \vv =0\text{?}\)
