Finding the Volume of a Parallelepiped In Exercises 69-72, find the volume V of the parallelepiped that has u , v , and w as adjacent edges using the formula V = | u ⋅ ( v × w ) | . u = − 2 i + j v = 3 i − 2 j + k w = 2 i − 3 j − 2 k
Finding the Volume of a Parallelepiped In Exercises 69-72, find the volume V of the parallelepiped that has u , v , and w as adjacent edges using the formula V = | u ⋅ ( v × w ) | . u = − 2 i + j v = 3 i − 2 j + k w = 2 i − 3 j − 2 k
Solution Summary: The author explains how to calculate the volume of parallelepiped using the given formula.
Finding the Volume of a ParallelepipedIn Exercises 69-72, find the volume
V
of the parallelepiped that has
u
,
v
, and
w
as adjacent edges using the formula
V
=
|
u
⋅
(
v
×
w
)
|
.
u
=
−
2
i
+
j
v
=
3
i
−
2
j
+
k
w
=
2
i
−
3
j
−
2
k
Finding the Volume of a Solid In Exercises 17-20, find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4.y =1/2x3, y = 4, x = 0
Exercise: Let u=[3,−2,1]�=[3,−2,1], v=[1,1,1]�=[1,1,1] and w=[2,−2,0]�=[2,−2,0].
The area of the parallelogram formed by u� and v� is A=√�=Answer 1 Question 14.
The volume of the parallelepiped formed by u,v�,� and w� is V=�=Answer 2 Question 14.
Given that the volume of a parallelepiped is the area of its base times its height, the height of the parallelepiped formed by u,v�,� and w� when its base is viewed as the parallelogram formed by u� and v� is h=ℎ=Answer 3 Question 14/√/Answer 4 Question 14.
The parallelepiped formed by u� and v� and ku×v��×� will have the same volume as the parallelepiped formed by u,v�,� and w� if k=±1/�=±1/x. what is x ?
Use the Trapezoidal Rule to estimate the number of square meters of land in a lot, where x and y are measured in meters, as shown in the figure. The land is bounded by a stream and two straight roads that meet at right angles.
x
0
100
200
300
400
500
600
700
800
900
1000
y
125
125
121
112
90
90
95
85
75
34
0
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