+0

# help asap

0
65
1

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
+5091
+2

$$\begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}2\\-3\end{pmatrix} t + \begin{pmatrix}1\\2\end{pmatrix}$$

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

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

.
Feb 5, 2019