Why is:

```
let a = new Vector3(0,0,0)
let b = new Vector3(0,0,0)
console.log(a.angleTo(b))
```

= to 1.57?

Why is:

```
let a = new Vector3(0,0,0)
let b = new Vector3(0,0,0)
console.log(a.angleTo(b))
```

= to 1.57?

We use the convention that the zero vector is orthogonal to every vector. More information about this topic here:

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Formally speaking, you cannot measure angles for vectors with 0 length … as they have no direction. However, by definition it is assumed that the angle between any vector and another 0-vector is 90° … which in radians is π/2 ≈ 1.57… This is a result of the dot product, which says, that if the dot product of two vectors is 0, then they are perpendicular. The dot product of any vector and a 0-vector is always 0. This is just a useful convention. Similar to the one that 0! is 1, not 0; and 0^{0} is 1.

2 Likes