Question: Suppose that u = (1, 2, 3), v = (3, 0, 2), w = (1, 3, 5) and k = 3. Show that a. u

Suppose that u = (1, 2, −3), v = (3, 0, 2), w = (1, −3, 5) and k = 3. Show that

a. u · v = v · u Just like multiplication, the dot product is commutative, i.e., the order doesn’t matter, and is distributive.

The dot product is also associative, but only with real numbers, not with other vectors.

b. u · (v + w) = u · v + u · w

c. k(u · v) = (ku) · v

d. v · v ≥ 0.

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