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owlet
 one year ago
For the ffg. lines in \(R^2\), determine a vector equation and parametric equations.
\(\Large x_2 = 3x_1 + 2\)
owlet
 one year ago
For the ffg. lines in \(R^2\), determine a vector equation and parametric equations. \(\Large x_2 = 3x_1 + 2\)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0introducing a parameter is easy  take \(x_1=t\), giving us the system; $$\left\{\begin{matrix}x_1=t&\\x_2=3t+2&\end{matrix}\right.$$ to get a vector equation, just use the above: $$r(t)=\langle x_1,x_2\rangle=\langle t,3t+2\rangle=t\langle 1,3\rangle +\langle0,2\rangle$$

owlet
 one year ago
Best ResponseYou've already chosen the best response.0where did you get (0,2)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0owlet, vector components are additive, so $$\langle a,b\rangle+\langle c,d\rangle=\langle a+c,b+d\rangle$$ and also multiplicative so $$\langle kx,ky\rangle =k\langle x,y\rangle$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which means $$\langle t,3t+2\rangle=\langle t,3t\rangle+\langle 0,2\rangle=t\langle 1,3\rangle+\langle0,2\rangle$$
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