Calculate the volume of a parallelepiped with sides give as
�
=
(
7,2
,
4
)
,
�
=
(
4,7
,
6
)
and
�
=
(
3,4
,
7
)
Select one:
125
cubic units
105
cubic units
135
cubic units
115
cubic units
A machine part consists of three heavy disks linked by struts of negligible weights as shown in the figure. Calculate the moment of inertia of the body about an axis through the centre of disk A and the kinetic energy, if the body rotates about an axis through A perpendicular to the plane of the diagram, with angular speed
�
=
6.0
�
�
�
�
-
1
..
Select one:
0.452kgm2
, 1.437 J
0.132kgm2
, 2.376 J
0.236kgm2
, 4.272 J
0.675kgm2
, 0.673 J
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n
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g
v
e
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t
i
c
a
l
t
e
x
t
i
s
?
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The volume of a parallelepiped with sides given by vectors a, b, and c is given by the absolute value of the scalar triple product (a x b) · c.
First, we find the cross product of vectors a and b:
a x b = |i j k|
|7 2 4|
|4 7 6|
= (2(6) - 4(7))i - (7(4) - 4(6))j + (7(7) - 2(4))k
= (-8)i - 10j + 45k
= (-8, -10, 45)
Then, we take the dot product of this cross product with vector c:
(-8, -10, 45) · (3, 4, 7) = (-8)(3) + (-10)(4) + (45)(7) = 125
So the absolute value of the scalar triple product and the volume of the parallelepiped is 125 cubic units.
Therefore, the correct answer is 125 cubic units.