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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
Question
If $\bar{a}=3 \hat{i}-\hat{\jmath}+4 \hat{k}, \bar{b}=2 \hat{i}+3 \hat{j}-\hat{k}, \bar{c}=5 \hat{i}+2 \hat{j}+3 \hat{k}$, then $\bar{a} \cdot(\bar{b} \times \bar{c})=\ldots \ldots$.
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Answer

$\begin{aligned} & \bar{a} \cdot(\bar{b} \times \bar{c})=\left|\begin{array}{ccc}3 & -1 & 4 \\ 2 & 3 & -1 \\ -5 & 2 & 3\end{array}\right| \\ & =3(9+2)+1(6-5)+4(4+15) \\ & =33+1+76 \\ & =110\end{aligned}$

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