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Problem Set #2
Score
Section:
C
REDIT
2
1
0
Problem # 1
.
Show that the points (
x
,
y
,
z
) which satisfy
x
2
+
y
2
+
z
2
=
4
y
– 2
z
are a sphere by rewriting this equation in the “standard” form for a sphere.
Identify explicitly the center and
the radius of the sphere.
C
REDIT
2
1
0
Problem # 2
.
Show that the points (
x
,
y
,
z
) which satisfy
x
2
+
y
2
+
z
2
– 6
x
+ 4
y
– 2
z
= 11
are a sphere by rewriting this equation in the “standard” form for a sphere.
Identify explicitly the center and
the radius of the sphere.
Math 32A
Lecture #5
Fall 2007

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Problem Set #2
C
REDIT
2
1
0
Problem # 3
.
Show that the following three points in 3
D
space:
A
= <–2,4,0>
B
= <1,2,–1>
C
= <–1,1,2>
form the vertices of an equilateral triangle.
C
REDIT
2
1
0
Problem # 4
.
Write, in the language of (2
D
) vectors the equation for the set of points
r
= <x,y> that form a
circle of radius
a
and is centered at the point
r
0
= <
x
0
,
y
0
>.
Your F
nal expression should involve only vectors,
vector–style symbols and the scalar
a
.