Work done by the force is 42 units which is correct option(C)
The work done by a force in moving along a vector that is the product of their.
Let the the object move from P(2,-4) to Q(10,1)
Here, the position vectors
[tex]\vec{p}[/tex] = [tex]2\vec {i}+(-4)\vec {j}[/tex], [tex]\vec{q}[/tex] = [tex]10\vec i+\vec{j}[/tex]
Hence [tex]\vec{PQ}[/tex] = [tex]\vec{q}[/tex] -[tex]\vec{p}[/tex] = [tex]10\vec i+\vec{j}[/tex] - [tex]2\vec {i}+(-4)\vec {j}[/tex],
[tex]\vec{PQ}[/tex] = [tex]8\vec i+5\vec{j}[/tex]
Force acts in a direction (4,2)
So [tex]\vec{F}[/tex] = [tex]4\vec i+2\vec{j}[/tex]
∴ Work done = [tex]\vec{F}.\vec{PQ}[/tex] = [tex](4\vec i+2\vec{j})[/tex] [tex].(8\vec i+5\vec{j})[/tex]
Work done = 32+10 =42 units
Hence work done by the force is 42 units
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