A) \[87\,\,unit\]
B) \[85\,\,unit\]
C) \[81\,\,unit\]
D) none of these
Correct Answer: A
Solution :
\[\therefore \]Displacement, \[\overset{\to }{\mathop{\mathbf{d}}}\,=(6-5)\widehat{\mathbf{i}}+(2+5)\widehat{\mathbf{j}}+(-2+7)\widehat{\mathbf{k}}\] \[=\widehat{\mathbf{i}}+7\widehat{\mathbf{j}}+5\widehat{\mathbf{k}}\] And total force\[\overset{\to }{\mathop{\mathbf{P}}}\,=\overset{\to }{\mathop{{{\mathbf{P}}_{\mathbf{1}}}}}\,+\overset{\to }{\mathop{{{\mathbf{P}}_{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{P}}_{\mathbf{3}}}}}\,\] \[=(10\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+11\widehat{\mathbf{k}})+(4\widehat{\mathbf{i}}+5\widehat{\mathbf{j}}+6\mathbf{\hat{k}})\] \[+(-2\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-9\widehat{\mathbf{k}})\] \[=12\widehat{\mathbf{i}}+5\widehat{\mathbf{j}}+8\widehat{\mathbf{k}}\] \[\therefore \]Work done\[W=\overset{\to }{\mathop{\mathbf{P}}}\,\cdot \overset{\to }{\mathop{\mathbf{d}}}\,\] \[=(12\widehat{\mathbf{i}}+5\widehat{\mathbf{j}}+8\widehat{\mathbf{k}})\cdot (\widehat{\mathbf{i}}+7\widehat{\mathbf{j}}+5\widehat{\mathbf{k}})\] \[=12+35+40=87\,\,unit\]
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