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Answer:

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


Practice

Here are some easily confirmed facts:

  1. (kv)·(kv) = k2v2   so   | 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.

QUESTION 3:

What is the length of the vector (30, 40)T ?