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Math 23, Spring 2005
B. Dodson
J. Mohler
1. Course Info
2. Week 1 Homework:
12.1, 12.2 Distance, vectors
Problem 12.1.15:
Show that the equation
x
2
+
y
2
+
z
2

6
x
+ 4
y

2
z
= 11
represents a sphere, and ﬁnd its center and radius.
Solution:
(
x

a
)
2
=
x
2

2
ax
+
a
2
,
so the terms
x
2

6
x
= (
x

3)
2

9
.
Likewise,
y
2
+ 4
y
=
. . .
z
2

2
z
=
. . .
y
2
+ 4
y
= (
y
+ 2)
2

4
z
2

2
z
= (
z

1)
2

1, so
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x
2
+
y
2
+
z
2

6
x
+ 4
y

2
z
=
(
x

3)
2

9 + (
y
+ 2)
2

4 + (
z

1)
2

1 = 11
,
or
(
x

3)
2
+ (
y
+ 2)
2
+ (
z

1)
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Unformatted text preview: 2 = 11 + 9 + 4 + 1 = 5 2 . conclusion: center = (3, 2, 1), radius = 5. Problem 12.2.19a: Find  ±a  and ±a2 ± b when ±a = < 6 , 2 , 3 >, ± b = <1 , 5 ,2 > . Solution: The length  ±a  = √ 36 + 4 + 9 = 7 , and ±a2 ± b = < 6 , 2 , 3 >2 <1 , 5 ,2 > = < 8 ,8 , 7 > ....
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This note was uploaded on 02/29/2008 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Vectors

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