The dot product is 4+1+1 = 6; so the length is √6.
Here are some easily confirmed facts:
= k2v2 so | kv| = k| v |
- | 0 | = 0
- 0 · v = 0
- | -v | = | v |
Here are those facts in English:
- If you scale a vector by a scalar k, you multiply its length by k.
- The length of the zero vector is zero.
- The dot product of the zero vector with any vector is zero.
- Reversing the direction of a vector does not change its length.
What is the length of the vector (30, 40)T ?