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Thread: explicit description of a line?

  1. #1
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    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?
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  2. #2
    Junior Member Nehushtan's Avatar
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    Re: Explicit description of a line?

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

    Quote Originally Posted by yangx View Post
    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 $\displaystyle (-2,3)$ is on the line $\displaystyle 3x+2y=0~.$
    That line contains $\displaystyle (0,0)$, so its direction vector is $\displaystyle <-2,3>$.

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

    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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