(a b) c Are the results same? Justify. - Vidyadip

Question

$(\bar{a} \times \bar{b}) \times \bar{c}$ Are the results same? Justify.

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Answer

$\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 1 & -2 & 0 \\ 1 & 2 & 0\end{array}\right|$

$\begin{aligned} & =(0-0) \hat{i}-(0-0) \hat{j}+(2-(-2)) \hat{k} \\ & =4 \hat{k}\end{aligned}$

$\therefore(\bar{a} \times \bar{b}) \times \bar{c}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 0 & 0 & 4 \\ 2 & 1 & -2\end{array}\right|$

$=(0-4) \hat{i}-(0-8) \hat{j}+(0-0) \hat{k}$

$=-4 \hat{i}+8 \hat{j}$

$\bar{a} \times(\bar{b} \times \bar{c}) \neq(\bar{a} \times \bar{b}) \times \bar{c}$

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