Direction of a vector of a line

Question

Suppose we have a line $x = 5$, and the vector $v_x<1, 0,-5>$.

How do I know which side of the line the vector is pointing to?

I am sorry if this has been asked before, I know it must be very trivial but I haven't managed to find a proper explanation anywhere.

Answer 1

Note that $x=5$ is not a line but a plane parallel to $yz$ plane passin through the point $(5,0,0)$. The vector $v_x<1, 0,-5>$ lies in the $xz$ plane with the $x$ component positive and $z$ component negative.

Answer 2

Chose for a given plane in $\mathbb R^3$ (or a line in two dimensions) one of its normal vectors $n$. Now the plane (the line) divides the space in two half spaces.

Given any vector $v$ (not orthogonal to the plane or line, resp.) calculate the dot product of $n$ and $v$. If the product is positive, then $v$ points to the same half space an $n$ does, otherwise in the other one.

In our special case we have $n=(1,0,0)$ and $v=(1,0,-5)$. Since their dot product equals $1$, $v$ points to the same half space as $n$ does.