How to find the volume of a parallelepiped?
Understand the Problem
The question is asking for the method to calculate the volume of a parallelepiped, which involves using vectors to determine its dimensions based on geometric principles.
Answer
|(a × b) ⋅ c|
The final answer is the volume of a parallelepiped is |(a × b) ⋅ c|
Answer for screen readers
The final answer is the volume of a parallelepiped is |(a × b) ⋅ c|
More Information
This formula derives from the geometric properties of vector operations, specifically using the scalar triple product to find volume.
Tips
Ensure vectors are correctly calculated for cross and dot products and take the absolute value for volume.
Sources
- Math Insight - Volume of a Parallelepiped - mathinsight.org
- Calculating the volume of a parallelepiped with vectors - Krista King Math - kristakingmath.com
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