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
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 ?
Exercise: Let u = [3, -2, 1], v = [1, 1, 1] and w = [2, -2,0].
The area of the parallelogram formed by u and v is A = √
The volume of the parallelepiped formed by u, v and w is =
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 = * √
x.
Check
The parallelepiped formed by u and v and ku x v will have the same volume as the parallelepiped formed by u, v and w
if k = +1/
x
x .
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