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 9.3.3 .
Determine each of the following:
(a) The length of the vector
\(\vu=\langle 1, 2, -3 \rangle\) using the dot product.
(b) The angle between the vectors
\(\vu =\langle 1, 2 \rangle\) and
\(\vv = \langle 4, -1 \rangle\) to the nearest tenth of a degree.
(c) The angle between the vectors
\(\vy =\langle 1, 2, -3 \rangle\) and
\(\vz = \langle -2, 1, 1 \rangle\) to the nearest tenth of a degree.
(d) If the angle between the vectors
\(\vu\) and
\(\vv\) is a right angle, what does the expression
\(\vu \cdot \vv = \vecmag{\vu} \vecmag{\vv} \cos(\theta)\) say about their dot product?
(e) If the angle between the vectors
\(\vu\) and
\(\vv\) is acute—that is, less than
\(\pi/2\) —what does the expression
\(\vu\cdot\vv=\vecmag{\vu}\vecmag{\vv}\cos(\theta)\) say about their dot product?
(f) If the angle between the vectors
\(\vu\) and
\(\vv\) is obtuse—that is, greater than
\(\pi/2\) —what does the expression
\(\vu\cdot\vv=\vecmag{\vu}\vecmag{\vv}\cos(\theta)\) say about their dot product?
