Objective: Get three of your symbol in a row (horizontally, vertically, or diagonally).
Gameplay: Each round, you are given two vector cards. You must use both cards by selecting a card and then a cell on the board. The cell's current vector will be replaced by the cross product of the selected card vector and the cell's vector.
The game uses the standard 3D unit vectors i, j, and k. The cross product of two vectors results in a third vector perpendicular to both. Remember the right-hand rule: if you point your index finger in the direction of the first vector and your middle finger in the direction of the second vector, your thumb points in the direction of the cross product.
Important: If a vector has a minus sign, the direction is reversed. For example, -i points in the opposite direction of i.
| × | i | j | k |
|---|---|---|---|
| i | 0 | k | -j |
| j | -k | 0 | i |
| k | j | -i | 0 |
When you cross i with j:
Using the right-hand rule: point your index finger right (i) and your middle finger up (j), your thumb points out of the screen (k).
When you cross j with i:
This is the opposite of the first example. The order matters in cross products!
When you cross i with -j:
The negative sign on j reverses the direction of the result.
When you cross a vector with itself:
Any vector crossed with itself results in the zero vector (0).