Skip to main content\(\newcommand{\avec}{{\mathbf a}}
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\)
In the background of this interactive diagram is a coordinate grid and a set of labelled axes. There are also two vectors
\(\vvec\) and
\(\wvec\) shown, both starting at the origin. There is also a set of lines, each of which is parallel to
\(\vvec\text{,}\) passing through integer multiples of
\(\wvec\text{.}\) In the same way, there is a second set of lines, each of which is parallel to
\(\wvec\text{,}\) passing through integer multiples of
\(\vvec\text{.}\) These two sets of parallel lines form a skewed coordinate grid.
Across the top of the diagram are two sliders, which can be used to vary two parameters labelled
\(c\) and
\(d\text{.}\) When one of those parameters is varied, the vector
\(c\vvec+d\wvec\) shown moving parallel to one of the sets of skewed grid lines.
Instructions.
The diagram below can be used to construct linear combinations whose weights \(c\) and \(d\) may be varied using the sliders at the top. The vectors \(\vvec\) and \(\wvec\) are outlined while the linear combination
\begin{equation*}
c\vvec + d\wvec
\end{equation*}
is shaded red.
