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Chapter 9: Q. 55 (page 628)

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脳B).C

Find the volume of a parallelepiped if the defining vectors are

A鈫�=3i^-2j^+4k^B鈫�=2i^+j^-2k^C鈫�=3i^-6j^-2k^

Short Answer

Expert verified

The volume is :

98cubicunits

Step by step solution

01

Step 1. given vectors

A鈫�=3i^-2j^+4k^B鈫�=2i^+j^-2k^C鈫�=3i^-6j^-2k^

02

Step 2. Volume of parallelopiped 

As given in question volume of parallelopiped is given by :

V=(A脳B).C

So , Using this :

A鈫�=3i^-2j^+4k^B鈫�=2i^+j^-2k^C鈫�=3i^-6j^-2k^V=(A脳B).CV=|((3i^-2j^+4k^)脳(2i^+j^-2k^)).(3i^-6j^-2k^)|V=|(0i^+14j^+7k^)>(3i^-6j^-2k^)|V=|-84-14|V=98cubicunits

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Most popular questions from this chapter

In Problems55鈥�66, the rectangular coordinates of a point are given. Find polar coordinates for each point.

3,0

An equation whose variables are polar coordinates is called a(n) ____ ______ .

Write the expression in the standard form a+bi.

3cos5蟺18+isin5蟺186

True or False The tests for symmetry in polar coordinates are necessary but not sufficient.

Match the graph with the polar equation

胃=3蟺4
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