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Determine the volume of the parallelepiped
for the given values of P, Q, and S.
- The formula for this solution is:
๐๐ = ๐ท๐ท โ (๐ธ๐ธ ร ๐บ๐บ). (Donโt forget units!)
- Why does this formula work? Think about
the de๏ฟฝinitions of dot and cross product.
P =
8i- j
talk
a
=
j
21
S
=
i
i
&
x Z
I
=
( +
x x)
(
+E
=
15
1
1((
=
3
((
x())
=
15i
3j
33K
(8i
9k)
(
;
j
36(2)
120
30
324
=
474
A crane is oriented so that the end of the 25-m
boom AO lies in the y-z plane. At the instant
shown, the tension in cable AB is 5.1 kN.
Determine the moment about each of the
coordinate axes of the force exerted on A by
cable AB.
- The moment we are interested in is the
moment of the crane (at O) about each axis.
- The moment about an axis requires we ๏ฟฝirst
determine the entire moment at a point that
lies on the axis. We need to see how the
crane at point O is experiencing a torque
along the x, y, and z axes. The ๏ฟฝirst step is to
๏ฟฝind the moment at O since it lies on all axes.
- The moment ๐ด๐ด ๐๐
is a vector with three
rotation components. To ๏ฟฝind the moment
about an axis, you can perform the dot
product of this moment with a unit vector
that describes the direction of the axis. In
this case, the i, j, and k axes (three separate
dot products). Is the result what you expect?
Y
A
ยท
is
n
C
As
= 25m
,
TABE .
/KN
.
Hi
= +[As
=
2 .
ift
= 15 .
2 m
Fix
/Fin
02
x
(A2)]
(AB)
20
m
5
,
100
2 . 8 :
14
15
. Z
j
Fish : Floo
Blog
No i S
is
I D
I
I
246 .
7
. 26
=
246
.
71i
