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If for $\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, then find [a b c $]$.
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Verified Answer
The correct answer is:
$-30$
Giveñ, åa $=2 \hat{\mathbf{i}}+3 \hat{\mathfrak{j}}+\hat{\mathbf{k}}, \hat{b}=\hat{\mathfrak{i}}-2 \hat{}$
and $\mathfrak{c}=-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$
$\therefore \quad[a \boldsymbol{b} c]=\left|\begin{array}{ccc}2 & 3 & 1 \\ 1 & -2 & 1 \\ -3 & 1 & 2\end{array}\right|$
$=2(-4-1)-3(2+3)+1(1-6)$
$=-10-15-5=-30$
and $\mathfrak{c}=-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$
$\therefore \quad[a \boldsymbol{b} c]=\left|\begin{array}{ccc}2 & 3 & 1 \\ 1 & -2 & 1 \\ -3 & 1 & 2\end{array}\right|$
$=2(-4-1)-3(2+3)+1(1-6)$
$=-10-15-5=-30$
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