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.