# Create a orthogonal Vector

For this we can use the dotproduct.

Example:

$V_1 = [1,6,2]$
$V_2 = ?$

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

$V_1 \cdot V_2 = 0$

Lets plugin our numbers

$1 * V_2x + 6 * V_2y + 2 *V_2z = 0$

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

$1*1+6*1+2*V_2z = 0$

$7+2V_2z = 0$

$V_2z = -3.5$

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

```