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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.2.6 .
(a) Let
\(\vu = \langle 2,3\rangle\) and
\(\vv = \langle -1,2\rangle\text{.}\) Find
\(\vecmag{\vu}\text{,}\) \(\vecmag{\vv}\text{,}\) and
\(\vecmag{\vu+\vv}\text{.}\) Is it true that
\(\vecmag{\vu+\vv} = \vecmag{\vu}+\vecmag{\vv}\text{?}\)
(b) Under what conditions will
\(\vecmag{\vw_1+\vw_2} = \vecmag{\vw_1}+\vecmag{\vw_2}\text{?}\)
Hint .
Think about how
\(\vw_1\text{,}\) \(\vw_2\text{,}\) and
\(\vw_1+\vw_2\) form the sides of a triangle.
(c) With the vector
\(\vu = \langle 2,3\rangle\text{,}\) find the lengths of
\(2\vu\text{,}\) \(3\vu\text{,}\) and
\(-2\vu\text{,}\) respectively, and use proper notation to label your results.
(d) In general, if
\(t\) is any scalar, how will
\(\vecmag{t \vw}\) be related to
\(\vecmag{\vw}\text{?}\)
(e) Of the vectors
\(\vi\text{,}\) \(\vj\text{,}\) and
\(\vi+\vj\text{,}\) which are unit vectors?
(f) Find a unit vector
\(\vv\) whose direction is the same as
\(\vu = \langle -2, 3\rangle\text{.}\)
(g) Find a unit vector
\(\vv\) in the opposite direction to
\(\vu = \langle -2, 3\rangle\text{.}\)
