The dot product is 4+1+1 = 6; so the length is √6.

Here are some easily confirmed facts:

- (k
**v**)**·**(k**v**) = k^{2}**v**so | k^{2}**v**| = 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} ?