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Answer:

Will |v|   =   √(v · v) ever be negative?     No, since length is always zero or positive.

Will it ever be zero?     Yes, when v is the zero vector.


Properties of Dot Product

Another property of the dot product is:

(au + bv) · w = (au) · w + (bv) · w, where a and b are scalars

Here is the list of properties of the dot product:

  1. u · v = |u||v| cos θ
  2. u · v = v · u
  3. u · v = 0 when u and v are orthogonal.
  4. 0 · 0 = 0
  5. |v|2 = v · v
  6. a (u·v) = (a u) · v
  7. (au + bv) · w = (au) · w + (bv) · w

QUESTION 8:

(Trick Question: ) What is u · v · w ?

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