Thread:

1. explicit description of a line?

Find an explicit description of the line 3x+2y = 0 in R2 through the origin.

the answer is:
span {[2, -3]} , but how?

2. Re: Explicit description of a line?

The line $3x+2y=0$ in $\mathbb R^2$ is spanned by any nonzero vector $\begin{pmatrix}x \\ y\end{pmatrix}$ such that $(x,y)$ lies on the line. $\begin{pmatrix}2 \\ -3\end{pmatrix}$ is one such vector; another would be $\begin{pmatrix}-1 \\ \frac32\end{pmatrix}$.

3. Re: explicit description of a line?

Originally Posted by yangx
Find an explicit description of the line 3x+2y = 0 in R2 through the origin.
the answer is: span {[2, -3]} , but how?
I do not necessarily disagree with reply #2.
However, the point $(-2,3)$ is on the line $3x+2y=0~.$
That line contains $(0,0)$, so its direction vector is $<-2,3>$.

Thus in traditional vector geometry its equation is $<0,0>+t<-2,3>~.$

So notation is everything here. Unless you tell us about the notation in use in your notes, we cannot really answer.
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