Volume of a Parallelepiped A parallelepiped is a prism whose faces are all parallelograms. Let A , B and C be the vectors that define the parallelepiped shown in the figure. The volume V of the parallelepiped is given by the formula V = | A × B ⋅ C | . Find the volume of a parallelepiped if the defining vectors are A = 3 i − 2 j + 4 k , B = 2 i + j − 2 k , and C = 3 i − 6 j − 2 k .
Volume of a Parallelepiped A parallelepiped is a prism whose faces are all parallelograms. Let A , B and C be the vectors that define the parallelepiped shown in the figure. The volume V of the parallelepiped is given by the formula V = | A × B ⋅ C | . Find the volume of a parallelepiped if the defining vectors are A = 3 i − 2 j + 4 k , B = 2 i + j − 2 k , and C = 3 i − 6 j − 2 k .
Solution Summary: The author explains that the volume of the parallelepiped for the defining vectors is 98 cubic units.
Volume of a Parallelepiped A parallelepiped is a prism whose faces are all parallelograms. Let
be the vectors that define the parallelepiped shown in the figure. The volume
of the parallelepiped is given by the formula
.
Find the volume of a parallelepiped if the defining vectors are
.
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.
Expert Solution
To determine
To find: The volume of the parallelepiped for the defining vectors are and
Answer to Problem 55AYU
Solution:
The volume of the parallelepiped is 98 cubic units
Explanation of Solution
Given:
; and
Formula used:
The volume of the parallelepiped is given by the formula
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