LinAlg4.2.15

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Find the volume of the parallelopiped whose edges are $\bar{i}+\bar{j}+\bar{k},\bar{i}-\bar{j}+\bar{k},\bar{i}+\bar{j}-\bar{k}\,$ .

Given edges of the parallelopiped are $\bar{i}+\bar{j}+\bar{k},\bar{i}-\bar{j}+\bar{k},\bar{i}+\bar{j}-\bar{k}\,$ .

Volume of the parallelopiped is $|[\bar{i}+\bar{j}+\bar{k},\bar{i}-\bar{j}+\bar{k},\bar{i}+\bar{j}-\bar{k}]|\,$ . which is equal to

$\begin{vmatrix} 1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{vmatrix}\,$

= $|1(1-1)-1(-1-1)+1(1+1)=|2+2|=4\,$ cubic units.

Main Page:Linear Algebra

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