A) \[41\widehat{\mathbf{i}}-8\widehat{\mathbf{j}}+55\widehat{\mathbf{k}}\]
B) \[-408\widehat{\mathbf{i}}-12\widehat{\mathbf{j}}+135\widehat{\mathbf{k}}\]
C) \[-36\widehat{\mathbf{i}}+14\widehat{\mathbf{j}}-35\widehat{\mathbf{k}}\]
D) None of the above
Correct Answer: B
Solution :
Let\[\overset{\to }{\mathop{\mathbf{F}}}\,=5\widehat{\mathbf{i}}+10\widehat{\mathbf{j}}+16\widehat{\mathbf{k}}\] Here,\[\overset{\to }{\mathop{\mathbf{r}}}\,=2\widehat{\mathbf{i}}-7\widehat{\mathbf{j}}+10\widehat{\mathbf{k}}-(-5\widehat{\mathbf{i}}+6\widehat{\mathbf{j}}-10\widehat{\mathbf{k}})\] \[=7\widehat{\mathbf{i}}-13\widehat{\mathbf{j}}+20\widehat{\mathbf{k}}\] \[\therefore \] Moment\[=\overset{\to }{\mathop{\mathbf{r}}}\,\times \overset{\to }{\mathop{\mathbf{F}}}\,\] \[=\left| \begin{matrix} \widehat{\mathbf{i}} & \widehat{\mathbf{j}} & \widehat{\mathbf{k}} \\ 7 & -13 & 20 \\ 5 & 10 & 16 \\ \end{matrix} \right|\] \[=\widehat{\mathbf{i}}(-208-200)-\widehat{\mathbf{j}}(112-100)\]\[+\widehat{\mathbf{k}}(70+65)\] \[=-408\widehat{\mathbf{i}}-12\widehat{\mathbf{j}}+135\widehat{\mathbf{k}}\]
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