A) \[25\,\,unit\]
B) \[-15\,\,unit\]
C) \[9\,\,unit\]
D) \[-9\,\,unit\]
Correct Answer: B
Solution :
Resultant force of the forces\[2\widehat{\mathbf{i}}-5\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\]\[-\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\]is given by \[\overset{\to }{\mathop{\mathbf{F}}}\,=(2\widehat{\mathbf{i}}-5\widehat{\mathbf{j}}+6\widehat{\mathbf{k}})+(-\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}})\] \[\overset{\to }{\mathop{\mathbf{F}}}\,=\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}+5\widehat{\mathbf{k}}\] and displacement \[\overset{\to }{\mathop{\mathbf{d}}}\,=\overset{\to }{\mathop{\mathbf{AB}}}\,=(6\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-3\widehat{\mathbf{k}})-(4\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}-2\widehat{\mathbf{k}})\] \[=2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\] Work done\[W=\overset{\to }{\mathop{\mathbf{F}}}\,\cdot \overset{\to }{\mathop{\mathbf{d}}}\,\] \[=(\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}+5\widehat{\mathbf{k}})\cdot (2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}-\widehat{\mathbf{k}})\] \[=2-12-5\] \[=-15\,\,unit\]
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