Not parallel to

It states that two lines, planes or vectors are not parallel. Parallel lines keep the same direction forever and, in a plane, never meet; the slash takes that away. So a ∦ b reads “a is not parallel to b”, and ∦ normally sits between the names of two objects.

What “not parallel” then implies depends on what a and b are. Two lines in the same plane that are not parallel cross at exactly one point. In three-dimensional space they may cross, or they may be skew: never meeting and never parallel either. Two nonzero vectors are not parallel when neither is a stretched or flipped copy of the other. Two planes in space that are not parallel cut each other along a line.

One thing it does not say is “perpendicular”. A line tilted by ten degrees and a line tilted by ninety are both ∦; the right-angle relation has its own sign, ⊥. You will meet ∦ in geometry lessons, homework answers, vector proofs and textbooks; it is a mathematical relation sign with no established chat meaning.

Where does the slashed sign come from?

It is ∥ with the standard negation slash. Mathematics negates a relation by striking through it: = becomes ≠, ∈ becomes ∉, ∣ becomes ∤. Unicode builds ∦ the same way; it defines the character as ∥ followed by a combining slash, which is why the two normally look the same on screen.

The parallel sign itself is old. Ancient Greek geometers such as Heron and Pappus marked “parallel” with two horizontal bars, the very shape later taken for equality when Robert Recorde introduced = in 1557. The bars were then stood upright, and the vertical ∥ appears in English mathematical books of 1673 and 1677. ∦ is simply the slash convention applied to that sign.