In Exercises 46 - 47 , three edges of a parallelepiped coincide with the position vectors for u , v , and w . Find the volume of the parallelepiped. u = [ 0 1 3 ] , v = [ − 2 1 0 ] , w = [ 0 4 1 ]
In Exercises 46 - 47 , three edges of a parallelepiped coincide with the position vectors for u , v , and w . Find the volume of the parallelepiped. u = [ 0 1 3 ] , v = [ − 2 1 0 ] , w = [ 0 4 1 ]
Solution Summary: The author explains how the volume of a parallelepiped is given by the absolute value of the scalar triple product of three vectors that represent the adjacent sides.
In Exercises
46
-
47
, three edges of a parallelepiped coincide with the position vectors for
u
,
v
, and
w
. Find the volume of the parallelepiped.
u
=
[
0
1
3
]
,
v
=
[
−
2
1
0
]
,
w
=
[
0
4
1
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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