Skip to main content\(\newcommand{\R}{\mathbb{R}}
\newcommand{\va}{\vec{a}}
\newcommand{\vb}{\vec{b}}
\newcommand{\vc}{\vec{c}}
\newcommand{\vC}{\vec{C}}
\newcommand{\vd}{\vec{d}}
\newcommand{\ve}{\vec{e}}
\newcommand{\cursedihat}{\hat{\dot{i}}}
\newcommand{\vi}{\hat{\imath}}
\newcommand{\vj}{\hat{\jmath}}
\newcommand{\vk}{\hat{k}}
\newcommand{\vn}{\vec{n}}
\newcommand{\vm}{\vec{m}}
\newcommand{\vr}{\vec{r}}
\newcommand{\vs}{\vec{s}}
\newcommand{\vu}{\vec{u}}
\newcommand{\vv}{\vec{v}}
\newcommand{\vw}{\vec{w}}
\newcommand{\vx}{\vec{x}}
\newcommand{\vy}{\vec{y}}
\newcommand{\vz}{\vec{z}}
\newcommand{\vzero}{\vec{0}}
\newcommand{\vF}{\vec{F}}
\newcommand{\vG}{\vec{G}}
\newcommand{\vH}{\vec{H}}
\newcommand{\vR}{\vec{R}}
\newcommand{\vT}{\vec{T}}
\newcommand{\vN}{\vec{N}}
\newcommand{\vL}{\vec{L}}
\newcommand{\vA}{\vec{A}}
\newcommand{\vB}{\vec{B}}
\newcommand{\vS}{\vec{S}}
\newcommand{\proj}{\text{proj}}
\newcommand{\comp}{\text{comp}}
\newcommand{\nin}{}
\newcommand{\vecmag}[1]{\left\lVert #1\right\rVert}
\newcommand{\grad}{\nabla}
\newcommand\restrict[2]{\raise-.5ex\hbox{$\Big|_{#1}^{#2}$}}
\DeclareMathOperator{\curl}{curl}
\DeclareMathOperator{\divg}{div}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
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\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
An interactive three dimensional plot with axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\text{.}\) Three sliders at the top of the figure allow the user to choose the value for
\(a\text{,}\) \(b\text{,}\) and
\(c\text{.}\) The values of
\(a\text{,}\) \(b\text{,}\) and
\(c\) change how far a black vector is drawn in the directions corresponding to the
\(x\text{,}\) \(y\text{,}\) and
\(z\) axes respectively. Magenta vectors of length a are drawn along the x axis and parallel to the x-axis in the xy-plane. Green vectors of length b are drawn along the y-axis and parallel to the y-axis at a distance a from the y-axis. Two blue vectors of length c are drawn parallel to the z-axis starting from the ends of the off axis magenta and green vectors and the origin. The values of The black vector,
\(\langle a,b,c \rangle\text{,}\) is decomposed into parts parallel to
\(\vi\text{,}\) \(\vj\text{,}\) and
\(\vk\text{.}\)