Question: If $\mathbf{a} = - 3\mathbf{i} + 7\mathbf{j} + 5\mathbf{k},$ \(\mathbf{b} = - 3\mathbf{i} + 7\math...

Question

If $\mathbf{a} = - 3\mathbf{i} + 7\mathbf{j} + 5\mathbf{k},$ $\mathbf{b} = - 3\mathbf{i} + 7\mathbf{j} - 3\mathbf{k}$ , $\mathbf{c} = 7\mathbf{i} - 5\mathbf{j} - 3\mathbf{k}$ are the three coterminous edges of a parallelopiped, then its volume is

Answer 1

Solution

Volume $= \left| \begin{matrix}

3 & 7 & 5 \
3 & 7 & - 3 \ 7 & - 5 & - 3 \end{matrix} \right|$

$= - 3( - 21 - 15) - 7(9 + 21) + 5(15 - 49)$

$= 180 - 210 - 170 = 272$ .

Question: If \(\mathbf{a} = - 3\mathbf{i} + 7\mathbf{j} + 5\mathbf{k},\) \(\mathbf{b} = - 3\mathbf{i} + 7\math...

Solution