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Consider the line parametrized by \(x=2t+1, y=-3t+2\)
Find a vector \(\begin{pmatrix}a\\b\end{pmatrix}\) that's parallel to this line and satisfies a+b=3.

 Feb 5, 2019
 #1
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\(\begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}2\\-3\end{pmatrix} t + \begin{pmatrix}1\\2\end{pmatrix}\)

 

\(\text{thus we are looking for a scaled version of the vector }\begin{pmatrix}2\\-3\end{pmatrix}\)

 

\( \begin{pmatrix}1&1\end{pmatrix}\cdot c\begin{pmatrix}2\\-3\end{pmatrix}=3\\ -c=3\\ c=-3\\ \begin{pmatrix}a\\b\end{pmatrix} = \begin{pmatrix}-6\\9\end{pmatrix}\)

.
 Feb 5, 2019

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