Math 215
Homework Set 2:
§§
12.4–13.2
Winter 2012
Most of the following problems are modified versions of the problems from your text book,
Multivariable
Calculus
, 7th ed., by James Stewart. Your solution to each problem should be complete, show all work,
and be written in complete sentences where appropriate. For
Maple
problems, include a printout that
shows all of the work and graphs that you generated in
Maple
to solve the problem, in addition to any
work you may have done by hand.
12.4.1: Let
a
be a vector whose
z
component is zero, and whose
x
 and
y
components are both positive,
such that

a

= 3
. Let
b
be a vector in the direction of
k
such that

b

= 4
. Sketch
a
and
b
with
initial point at the origin in the 3 dimensional Cartesian coordinate system.
(a) Find

a
×
b

.
(b) Use the right hand rule to determine whether the components of
a
×
b
are positive, negative,
or zero.
12.4.2: Find two unit vectors orthogonal to both
2
i
+ 2
j

k
and

j
+
k
. Are there any others? Explain.
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 Fall '08
 Fish
 Calculus, Cartesian Coordinate System, Parametric Equations, cylinder x2, Parametric equation, dimensional Cartesian coordinate

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