Is this function for cross product right?

[warped_wart_wars]

This:

class Point:
    ...
    def cross_product(self, other):
        return self.x * other.y - self.y * other.x
    ...

It returns a scalar, which isn't quite right, but since this is working on 2D Points, you can probably just treat it as a scalar, because the cross product of two 2D points is (0, 0, someZ).

Solution:

@warped_wart_wars

I found this post I made, and it confirms that the answer to the topic of this post is "yes".

@warped_wart_wars

Ah. But for $$a$$ and $$b$$ I only have 2D vectors, so $$c$$, the cross product, would have an x coordinate of $$a_y0-0b_y=0-0=0$$ and a y coordinate of $$0b_x-a_x0=0-0=0$$, so the cross product of two 2D vectors would be $$(0,0,a_xb_y-a_yb_x)$$, which could be represented as a single number.

[programmer_user]

Calculating a 2D Vector's Cross Product

TL;DR You can't compute the cross product of 2 2d vectors.

[warped_wart_wars]

You can, technically, if you treat the 2D vectors as 3D vectors with z of zero.

[programmer_user]

If you read the answer, then

However, often it is interesting to evaluate the cross product of two vectors assuming that the 2D vectors are extended to 3D by setting their z-coordinate to zero. This is the same as working with 3D vectors on the xy-plane.

If you extend the vectors that way and calculate the cross product of such an extended vector pair you'll notice that only the z-component has a meaningful value: x and y will always be zero.

the scalar version is the hack

[warped_wart_wars]

I found this post I made, and it confirms that the answer to the topic of this post is "yes".

@warped_wart_wars

Ah. But for $$a$$ and $$b$$ I only have 2D vectors, so $$c$$, the cross product, would have an x coordinate of $$a_y0-0b_y=0-0=0$$ and a y coordinate of $$0b_x-a_x0=0-0=0$$, so the cross product of two 2D vectors would be $$(0,0,a_xb_y-a_yb_x)$$, which could be represented as a single number.