Calculus: The Language of Change

Exercise Set 15.2
Position Vectors

solutions by Randall Childs and David Theobald

See the labeled Mathematica notebooks to solve Computer Exercises 1, 2, and 3.

Exercise 4

Find the ordered pairs or triples designating the following position vectors.

Answers:
	(a)	(3,2)
	(b)	(3,-1)
	(c)	(-2,4,2)
	(d)	(1.5,-3,1)

Explanations:
	Nothing fancy here.  The values of the coordinates are just what they appear to be.  The only moderately tricky part is keeping track of which coordinate is listed first, second, etc.

Exercise 5

Answers will vary.  But here are some rough guidelines and fun (maybe) questions.

For part (a) none of your answers should have negative coordinates.  Why not?  Where would an object be if it had a zero for one of its coordinates?

For part (b) none of your answers to (1)-(4) should have negative coordinates for the same reason as for part (a).  For the front door of the building and your parent's home, at least one of the coordinates is likely to be negative.  Which coordinate (for the front door) must be negative if your classroom is on the seventh floor?  What if your classroom were in Colorado and your parents live in Miami?  Or vice versa?  Does it matter on which floor you or your parent's home is?  What happens to the coordinates of points outside of the classroom if you choose a different corner as the origin of your axes?