Comment by quietbritishjim

I found the "perp dot product" an interesting one. It's a pity the description is in a massive pdf (though it looks like a great book). The top Google result is the MathWorld page [1] but it's very brief.

Here how that pdf describes it. It first defines the perpendicular operator on a 2D vector x as

  x⟂ := (-x_2, x_1)

which is x rotated 90 degrees anticlockwise. Then the perp dot product of two 2D vectors is defined as

  x⟂ . y

This has a few interesting properties, most notably that

  x⟂ . y = |x| |y| sin θ

For example, the sign of the perp dot product tells you whether you need to rotate clockwise or anticlockwise to get from x to y. If it's zero then they're parallel – could be pointing in same or opposite directions (or over or both are zero).

In this Reddit post [2] about it, again not much is said, but a redditor makes the astute observation:

> The perp dot product is the same as the cross product of vectors in a plane, except that you take the magnitude of the z component and ignore the x/y components (which are 0).

[1] http://mathworld.wolfram.com/PerpDotProduct.html

[2] https://www.reddit.com/r/learnmath/comments/agfm8g/what_is_p...