A) 1 unit
B) 20 unit
C) 5 unit
D) zero
Correct Answer: A
Solution :
Work (W) is measured by the vector product of the applied force \[(\vec{F})\]and the displacement \[(\vec{s})\] of the body in the direction of the force \[(\vec{F}),\] that is, \[W=\vec{F}.\vec{s}\] Given, \[\vec{F}=2\hat{i}+3\hat{j}-5\hat{k},\,\hat{s}=2\hat{i}+4\hat{j}+3\hat{k}\] \[\therefore \] \[W=(2\hat{i}+3\hat{j}-5\hat{k}).(2\hat{i}+4\hat{j}+3\hat{k})\] \[=(2)(2)+(3)(4)+(-5)(3)\] \[=4+12-15\] \[=1\,\text{unit}\] Note: Both force and displacement are vector quantities but work is a scalar quantity.
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