notes/Resources/mathematics/geometry/euclidean.md

# Create a orthogonal Vector

For this we can use the dotproduct.

Example:

```latex
V_1 = [1,6,2] \\
V_2 = ?
```

We know that the dot product of these two vectors must be zero, we can use that

```latex
V_1 \cdot V_2 = 0
```

Let's plug in our numbers

```latex
1 * V_2x + 6 * V_2y + 2 *V_2z = 0
```

Lets choose arbitrary numbers for $V_2x$ and $V_2y$, for now $1$ because that makes the calculation a bit easier

```latex
1*1+6*1+2*V_2z = 0
```
```latex
7+2V_2z = 0

V_2z = -3.5
```

```ts
// Note the the resulting vector can be very large
function findOrthogonalVector([x,y,z]:number[]){
	return [1,1,-((x+y)/z)]
}

```