I've been doing some work where I've needed to talk about vectors that are parallel and those that are antiparallel, parallel to the negative of the other vector.
Is there a symbol for this?
I can write $A\parallel B$ for parallel, $A \not\parallel B$ for not parallel. Is there a symbol for writing antiparallel without having to write $A\parallel-B$ ?
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Edit: this is of use in physics, where, for instance, you can talk about spins which are parallel (both up or down) and spins which are antiparallel (one up and one down).
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$\begingroup$I belive that when we talk about vectors you can use $a \uparrow\uparrow b$ for parallel vectors and $a \uparrow\downarrow b$ for antiparallel.
$\endgroup$ 8 $\begingroup$I think you should consider using a symbol that shows your meaning of "parallelism". Could try these two couple: $v \mathrel{{{\upharpoonleft}{\downharpoonright}}} w$ or $v\mathrel{\uparrow\downarrow}w$ as opposite to positively-parallel: $v\mathrel{{{\upharpoonleft}{\upharpoonright}}}w$ or $v\mathrel{\uparrow\uparrow}w$ Hope it helps
$\endgroup$ 8 $\begingroup$There isn't such a symbol (as far as I know) because if $v\|w$ then $-v\|w$ as well. Indeed each vector is parallel to its own opposite, as you take only the line on which it lies, when you speak of direction. (To describe that fact you however can write $v\in\mathbb{R}^{-}w$ in an opposite way of "positive" parallelism:$v\in\mathbb{R}^+w$)
$\endgroup$ 2 $\begingroup$The "hat" symbol denotes a unit vector pointing in the original vector's direction
So if you say $\hat{A}=-\hat{B}$, then that means that the vectors are in opposite directions. You could also say that A and -B are parallel.
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