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owlet

  • one year ago

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

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  1. owlet
    • one year ago
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    @Luigi0210

  2. owlet
    • one year ago
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    @nincompoop

  3. owlet
    • one year ago
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    @mathmate

  4. anonymous
    • one year ago
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    introducing 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: $$r(t)=\langle x_1,x_2\rangle=\langle t,3t+2\rangle=t\langle 1,3\rangle +\langle0,2\rangle$$

  5. owlet
    • one year ago
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    where did you get (0,2)?

  6. anonymous
    • one year ago
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    owlet, vector components are additive, so $$\langle a,b\rangle+\langle c,d\rangle=\langle a+c,b+d\rangle$$ and also multiplicative so $$\langle kx,ky\rangle =k\langle x,y\rangle$$

  7. anonymous
    • one year ago
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    which means $$\langle t,3t+2\rangle=\langle t,3t\rangle+\langle 0,2\rangle=t\langle 1,3\rangle+\langle0,2\rangle$$

  8. owlet
    • one year ago
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    aah okay. thanks.

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