An object is diplaced from the position vector r= (2 i  +  3j )m to R = ( 4 j  +  6 k )

under a force F= (3 x^2 i +  2y j )N . Find the work done by force.

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RATES ARE ASSURED!!

W=F.d  (dot product)

now F=3x^2 i + 2y j

d=(4 i +6 j )-  (2i+3j)

d=2i+3j

therefore

W=(3x^2i+2yj).(2i+3j)

W=6x^2+6y  ans.

F = 3 x^2 i + 2yj

r(positon vector) = dx i + dy j + dz k

w= intg(3 x^2 ) dx + intg (2y) dy

work = x^3( limit from 2 to 0) +y^2(limit from 3 to 4)

work = 0^3 - 2^3 + 4^2 - 3^2

w= -1 J