**Problem 1**. Compute the magnitude of the vector and compute the magnitude of the vector where .

**Problem 2**. (a) Draw a picture of the vector in standard position in .

(b) Find all numbers so that (from part (a) above) is perpendicular to the vector . Once you have found all possible values for , pick one and draw the vector in the same picture you from part (a) where you drew the vector .

**Problem 3**. (a) Draw a picture of the set of points defined by

(b) Draw a picture of the set of points defined by

**Problem 4**. Complete the definition of the **dot product** between two vectors where and :

**Problem 5**. Exercise 1 from Section 9.3 of our textbook.

**Problem 6**. Exercise 3 from Section 9.3 of our textbook.

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