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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 \(a+b=3\).

 Oct 9, 2019
 #1
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\(v = \alpha\begin{pmatrix}2\\-3\end{pmatrix},~\alpha \in \mathbb{R}\\ 2\alpha - 3\alpha = 3\\ \alpha = -3\\ v = \begin{pmatrix}-6\\9\end{pmatrix}\)

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 Oct 9, 2019

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