Use the Triple Scalar Product to Find the Volume of the Parallelepiped

question 61

Multiple Choice

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. $$\begin{array} { l } \mathbf { u } = ( 9,9,0 ) \\\mathbf { v } = ( 0,0 , - 9 ) \\\mathbf { w } = ( 9,0,9 ) \end{array}$$ $$\mathrm { a } = ( 9,9,0 ) , \mathrm { b } = ( 0,0 , - 9 ) , \mathrm { c } = ( 9,0,9 )$$

• A) \(\text { Volume } = 730 \text { cubic units }\)
• B) \(\text { Volume } = 731 \text { cubic units }\)
• C) \(\text { Volume } = 733 \text { cubic units }\)
• D) \(\text { Volume } = 729 \text { cubic units }\)
• E) \(\text { Volume } = 732 \text { cubic units }\)

---

Definitions:

Biomass Pyramid

A graphical representation showing the relative amount of living organic matter available at each trophic level in an ecosystem.

Anaerobic Respiration

A process by which organisms produce energy without the use of oxygen.

Pyramid of Biomass

A graphical representation showing the total mass of living organisms at each trophic level in an ecosystem.

Tropical Rainforest

An ecosystem characterized by high rainfall, lush vegetation, and a diverse array of plant and animal species, critical for producing oxygen and storing carbon dioxide.