This preview shows page 1. Sign up to view the full content.
Solutions of CalcIII Quiz 2
September 20, 2006
1. The volume is the absolute value of the determinant

3 0 1

2 1 1
1
1 1
which
is 6
2. Let us assume
D
has coordinates (
x
0
,y
0
,z
0
). The volume is the absolute
value of the determinant

3
0
1

2
1
1
x
0
y
0
z
0
which is
x
0
+ 2
y
0
+ 3
z
0
. Since
D
is on the plane
x
+ 2
y
+ 3
z
= 6, we have
x
0
+ 2
y
0
+ 3
z
0
= 6.
3. The volume of the parallelepiped is given by the product of the area of
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: the parallelogram determined by→ OA and→ OB and its height. Both A and B are on the plane x + 2 y + 3 z = 0 to which x + 2 y + 3 z = 6 is parallel. Therefore, for any point D on the plane x + 2 y + 3 z = 6, the height of the parallelepiped is the same. 1...
View
Full
Document
This note was uploaded on 11/02/2009 for the course MATH V1201 taught by Professor Perutz during the Spring '08 term at Columbia.
 Spring '08
 Perutz
 Determinant

Click to edit the document details