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Chapter 9: Q. 56 (page 628)

Find the volume of a parallelepiped whose defining vectors are

A鈫�=1,0,6B鈫�=2,3,-8C鈫�=8,-5,6

Short Answer

Expert verified

The volume is : 226 cubic units

Step by step solution

01

Step 1. given vectors

A鈫�=1,0,6B鈫�=2,3,-8C鈫�=8,-5,6

Which can be written as :

A鈫�=i^+0j^+6k^B鈫�=2i^+3j^-k^C鈫�=8i^-5j^+6k^

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�=i^+0j^+6k^B鈫�=2i^+3j^-8k^C鈫�=8i^-5j^+6k^V=(A脳B).CV=|((i^+0j^+6k^)脳(2i^+3j^-8k^)).(8i^-5j^+6k^)|V=|(-18i^+20j^+3k^)脳(8i^-5j^+6k^)|V=|-144-100+18|V=226cubicunits

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