A) \[\text{-7}\widehat{\text{i}}\text{-8}\widehat{\text{j}}\text{-4}\widehat{\text{k}}\]
B) \[\text{-4}\widehat{\text{i}}\text{-}\widehat{\text{j}}\text{-8}\widehat{\text{k}}\]
C) \[\text{-8}\widehat{\text{i}}\text{-4}\widehat{\text{j}}\text{-7}\widehat{\text{k}}\]
D) \[\text{-7}\widehat{\text{i}}\text{-4}\widehat{\text{j}}\text{-8}\widehat{\text{k}}\]
Correct Answer: D
Solution :
[d] |
\[\overrightarrow{\tau }=(\overrightarrow{r}-{{\overrightarrow{r}}_{0}})\times \overrightarrow{\text{F}}\] (i) |
\[\overrightarrow{r}-{{\overrightarrow{r}}_{_{0}}}=(2\widehat{\text{i}}-0\widehat{\text{j}}-3\widehat{\text{k}})-(2\widehat{i}-2\widehat{\text{j}}-2\widehat{\text{k}})\] |
\[=0\widehat{\text{i}}+2\widehat{\text{j}}-\widehat{\text{k}}\] |
\[\overrightarrow{\tau }=\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 0 & 2 & -1 \\ 4 & 5 & -6 \\ \end{matrix} \right|=-7\widehat{i}-4\widehat{j}-8\widehat{k}\] |
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