Question

For the ffg. lines in \(R^2\), determine a vector equation and parametric equations.

\(\Large x_2 = 3x_1 + 2\)

Answer 1

@Luigi0210

Answer 2

@nincompoop

Answer 3

@mathmate

Answer 4

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: $$r(t)=\langle x_1,x_2\rangle=\langle t,3t+2\rangle=t\langle 1,3\rangle +\langle0,2\rangle$$

Answer 5

where did you get (0,2)?

Answer 6

owlet, vector components are additive, so $$\langle a,b\rangle+\langle c,d\rangle=\langle a+c,b+d\rangle$$ and also multiplicative so $$\langle kx,ky\rangle =k\langle x,y\rangle$$

Answer 7

which means $$\langle t,3t+2\rangle=\langle t,3t\rangle+\langle 0,2\rangle=t\langle 1,3\rangle+\langle0,2\rangle$$

Answer 8

aah okay. thanks.