Math 232 Spring 2009 Study Sheet for Test 1
Test questions may come from homework problems, and all examples and
material covered in class. You are responsible for basic proofs at the level
covered in homework and class. You should know all definitions given in class or
in the text. You should know how to use the results of any theorem in the text.
There may be True-False questions.
Text Section and Topics Assigned problems
10.1 Vectors in the Plane: vectors,
components, magnitude, position vector,
unit vectors and Theorems.
W: 3 E: 33,34,38,48,49
10.2 Vectors in Space: vectors,
components, magnitude, position vector,
unit vectors and Theorems
W: 2,4 E: 12,
22,23,28,40,48,59,63
10.3 Dot Product: dot product, angle
between vectors, Cauchy-Schwarz and
Triangle Inequalities, components,
projections, and Theorems.
6, 10, 16, 23, 24, 33,,34, 35,
50, 55, 61
10.4 The Cross Product: determinant of a
matrix, cross product, angle between
vectors and Theorems.
4, 10, 16, 19, 21, 41-46
10.5 Lines and Planes in Space:
parametric and symmetric equations for the
line, general equation and the linear
equation for a plane, the distance between
parallel planes and Theorems.
2, 6, 12, 16, 21, 31, 33, 54,
55-62
SAMPLE TEST PROBLEMS [numbers in brackets are points]
Show your work and circle your answers when appropriate. No work, no
credit. Points for each question are in [brackets] to the right of the
question number or letter. Work only one of questions 13 and 14.
Circle True or False and give your reasons. [2 points each]
1. True False If
0a b
then
0a b
.
2. True False
( ) ( )a b c a b c
3. True False
( ) 0a b b a
4. True False
( ) ( )a b c b a c a
5. True False For any vectors
a
and
b
,
a b a b
.
6. [10 points] Using the definitions of vector addition, vector subtraction and
scalar multiplication in
3
V
, prove that
( ) ( )k a b c k a b c
, where k is a
scalar.
