Skip to main content
Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
\newcommand{\va}{\vec{a}}
\newcommand{\vb}{\vec{b}}
\newcommand{\vc}{\vec{c}}
\newcommand{\vC}{\vec{C}}
\newcommand{\vd}{\vec{d}}
\newcommand{\ve}{\vec{e}}
\newcommand{\cursedihat}{\hat{\dot{i}}}
\newcommand{\vi}{\hat{\imath}}
\newcommand{\vj}{\hat{\jmath}}
\newcommand{\vk}{\hat{k}}
\newcommand{\vn}{\vec{n}}
\newcommand{\vm}{\vec{m}}
\newcommand{\vr}{\vec{r}}
\newcommand{\vs}{\vec{s}}
\newcommand{\vu}{\vec{u}}
\newcommand{\vv}{\vec{v}}
\newcommand{\vw}{\vec{w}}
\newcommand{\vx}{\vec{x}}
\newcommand{\vy}{\vec{y}}
\newcommand{\vz}{\vec{z}}
\newcommand{\vzero}{\vec{0}}
\newcommand{\vF}{\vec{F}}
\newcommand{\vG}{\vec{G}}
\newcommand{\vH}{\vec{H}}
\newcommand{\vR}{\vec{R}}
\newcommand{\vT}{\vec{T}}
\newcommand{\vN}{\vec{N}}
\newcommand{\vL}{\vec{L}}
\newcommand{\vB}{\vec{B}}
\newcommand{\vS}{\vec{S}}
\newcommand{\proj}{\text{proj}}
\newcommand{\comp}{\text{comp}}
\newcommand{\nin}{}
\newcommand{\vecmag}[1]{\left\lVert #1\right\rVert}
\newcommand{\grad}{\nabla}
\newcommand\restrict[1]{\raise-.5ex\hbox{$\Big|$}_{#1}}
\DeclareMathOperator{\curl}{curl}
\DeclareMathOperator{\divg}{div}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Activity 9.2.5 .
Suppose that
\(\vu\) and
\(\vv\) are the vectors shown in
Figure 9.2.8 .
(a) Sketch sums (b) Sketch multiples Figure 9.2.8. Left: Sketch sums. Right: Sketch multiples.
(a) On the axes in
Figure 9.2.8.(a) , sketch the vectors
\(\vu + \vv\text{,}\) \(\vv - \vu\text{,}\) \(2\vu\text{,}\) \(-2\vu\text{,}\) and
\(-3\vv\text{.}\)
(b) What are the components of
\(0\vv\text{?}\)
(c) On the in
Figure 9.2.8.(b) , sketch the vectors
\(-3\vv\text{,}\) \(-2\vv\text{,}\) \(-1\vv\text{,}\) \(2\vv\text{,}\) and
\(3\vv\text{.}\)
(d) Give a geometric description of the set of terminal points of the vectors
\(t\vv\) where
\(t\) is any scalar.
(e) On the set of axes in
Figure 9.2.8.(b) , sketch the vectors
\(\vu-3\vv\text{,}\) \(\vu-2\vv\text{,}\) \(\vu-\vv\text{,}\) \(\vu + \vv\text{,}\) and
\(\vu + 2\vv\text{.}\)
(f) Give a geometric description of the set of terminal points of the vectors
\(\vu + t\vv\) where
\(t\) is any scalar.
