Question
Find the volume of a parallelopiped whose coterminus edges are represented by the
vector $\hat{j}+\hat{k} \cdot \hat{i}+\hat{k}$ and $\hat{i}+\hat{j}$. Also find volume of tetrahedron having these
coterminous edges.
vector $\hat{j}+\hat{k} \cdot \hat{i}+\hat{k}$ and $\hat{i}+\hat{j}$. Also find volume of tetrahedron having these
coterminous edges.
Then volume of the parallelopiped $=[\bar{a} \bar{b} \bar{c}]$
$=\left|\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right|$
= 0(0 – 1) – 1(0 – 1) + 1(1 – 0) = 0 + 1 + 1 = 2cu units.
Also, volume of tetrahedron $=\frac{1}{6}[\bar{a} \bar{b} \bar{c}]$
$=\frac{1}{6}(2)=\frac{1}{3}$ cubic units.
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