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If the vectors $2 \mathbf{i}-3 \mathbf{j}, \mathbf{i}+\mathbf{j}-\mathbf{k}$ and $3 \mathbf{i}-\mathbf{k}$ form three concurrent edges of a parallelopiped, then the volume of the parallelopiped is
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Verified Answer
The correct answer is:
4
Here,
$\begin{aligned}
& \overrightarrow{O A}=2 \mathbf{i}-3 \mathbf{j}=\mathbf{a} \quad \text { (say) } \\
& \overrightarrow{O B}=\mathbf{i}+\mathbf{j}-\mathbf{k}=\mathbf{b} \quad \text { (say) }
\end{aligned}$
and
$\overrightarrow{O C}=3 \mathbf{i}-\mathbf{k}=\mathbf{c} \quad \text { (say) }$
Hence volume is $[\mathbf{a} \mathbf{b} \mathbf{c}]=\mathbf{a} \cdot(\mathbf{b} \times \mathbf{c})=\left|\begin{array}{ccc}2 & -3 & 0 \\ 1 & 1 & -1 \\ 3 & 0 & -1\end{array}\right|=4$
$\begin{aligned}
& \overrightarrow{O A}=2 \mathbf{i}-3 \mathbf{j}=\mathbf{a} \quad \text { (say) } \\
& \overrightarrow{O B}=\mathbf{i}+\mathbf{j}-\mathbf{k}=\mathbf{b} \quad \text { (say) }
\end{aligned}$
and
$\overrightarrow{O C}=3 \mathbf{i}-\mathbf{k}=\mathbf{c} \quad \text { (say) }$
Hence volume is $[\mathbf{a} \mathbf{b} \mathbf{c}]=\mathbf{a} \cdot(\mathbf{b} \times \mathbf{c})=\left|\begin{array}{ccc}2 & -3 & 0 \\ 1 & 1 & -1 \\ 3 & 0 & -1\end{array}\right|=4$
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