Practice

Here are some easily confirmed facts:

1. (kv)·(kv) = k²v² ...... ie. | kv| = k| v |
2. | 0 | = 0
3. 0 · v = 0
4. | -v | = | v |

Here are those facts in English:

1. If you scale a vector by a scalar k, you multiply its length by k.
2. The length of the zero vector is zero.
3. The dot product of the zero vector with any vector is zero.
4. Reversing the direction of a vector does not change its length.