## On the Subject of Vectors

Uhhh... What's with the floating 3D arrows?

This module has a 3D display of a 3-dimensional graph with the axes x, y, and z, an auto-scrolling display, a button with a display on it, and 3 LEDs.

The 3D display will have between 1-3 vectors (3D arrows) on it. The vectors will be a different color than the axes on the graph, and the axes are always white and have a letter indicating which axis they are. The auto-scrolling display will be cycling through all the data about each vector. The data values it displays are the color of the vector in the graph, the vector's magnitude, and the vector's components. The button with a display can be held down, and will display how long it has been held for on the display.

To solve this module, the button with a display must be held down for a certain amount of time and released when this time is reached. If this is done right it will count as a correct input, lighting up an LED green and moving on to the next stage, a new set of vectors will be generated each stage. If the button is held for the correct amount of time for 3 stages the module will be disarmed. If the button is held for an incorrect amount of time upon release a strike WILL be recorded and the current stage will reset (new vectors and will not move back a stage). In order to figure out the time to hold the button down for determine how many vectors the graph has and use the corresponding section to get further instructions. If you have 1 vector, use the section '**1 Vector**'. If you have more than 1 vector use the section '**Multiple Vectors**'.

### 1 Vector

If 1 vector is on the graph then the auto-scrolling display will not be scrolling and will stay on the info for this vector. One of the pieces of data about this vector is missing and must be calculated (the color can never be missing). Keep in mind when performing calculations with vector components they can be positive or negative. To determine whether a component is positive or negative, reference the 3D graph. If the vector's arrow points in the direction of a negative axis, then the component is negative. Otherwise, it is positive. A vector's magnitude is always positive.

#### If the magnitude is missing...

Plug all known values into this equation and solve for M (rounding to the nearest tenth), where M is the missing magnitude and x/y/z are the components: **M = √(x ^{2}+y^{2}+z^{2})**