\(\newcommand{\R}{\mathbb{R}} \newcommand{\va}{\vec{a}} \newcommand{\vb}{\vec{b}} \newcommand{\vc}{\vec{c}} \newcommand{\vC}{\vec{C}} \newcommand{\vd}{\vec{d}} \newcommand{\ve}{\vec{e}} \newcommand{\cursedihat}{\hat{\dot{i}}} \newcommand{\vi}{\hat{\imath}} \newcommand{\vj}{\hat{\jmath}} \newcommand{\vk}{\hat{k}} \newcommand{\vn}{\vec{n}} \newcommand{\vm}{\vec{m}} \newcommand{\vr}{\vec{r}} \newcommand{\vs}{\vec{s}} \newcommand{\vu}{\vec{u}} \newcommand{\vv}{\vec{v}} \newcommand{\vw}{\vec{w}} \newcommand{\vx}{\vec{x}} \newcommand{\vy}{\vec{y}} \newcommand{\vz}{\vec{z}} \newcommand{\vzero}{\vec{0}} \newcommand{\vF}{\vec{F}} \newcommand{\vG}{\vec{G}} \newcommand{\vH}{\vec{H}} \newcommand{\vR}{\vec{R}} \newcommand{\vT}{\vec{T}} \newcommand{\vN}{\vec{N}} \newcommand{\vL}{\vec{L}} \newcommand{\vB}{\vec{B}} \newcommand{\vS}{\vec{S}} \newcommand{\proj}{\text{proj}} \newcommand{\comp}{\text{comp}} \newcommand{\nin}{} \newcommand{\vecmag}[1]{\left\lVert #1\right\rVert} \newcommand{\grad}{\nabla} \newcommand\restrict[1]{\raise-.5ex\hbox{$\Big|$}_{#1}} \DeclareMathOperator{\curl}{curl} \DeclareMathOperator{\divg}{div} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)

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Activity 9.2.4.

In this activity, use Properties of vector operations to simplify each of the following expressions into a single vector of the form $\langle a,b,c \rangle\text{.}$ For this activity, let $\vu=\langle 1,-2,3 \rangle\text{,}$ $\vv=\langle 2,-2,5\rangle\text{,}$ and $\vw=\langle -3,0,3\rangle\text{.}$

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(a)

$\vu+2\vv+3\vw$

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(b)

$2\vw-3\vu$

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(c)

$-4(\vv-\vw)$

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(d)

$-2(3\vu)$