Calculate the work done to displace the particle from
(1,2) to (4,5). If `vec(F) = 4hat(i) + 3hat(j)`

Explanation

dw = `vec(F).d vec(r ) (d vec(r ) = dx vec(i) + dh hat(j) + dz hat(k))`
dw = `(4hat(i) + 3 hat(j)). (dx hat(i) + dy hat(j)) " " rArr " " dw = 4dx + 3dy `
`int_(0)^(w) dw = int_(1)^(4) 4dx + int_(2)^(5) 3dy rArr w = [ 4x]_(1)^(4) + [3 y ]_(2)^(5)`
w = (16 - 4) + (15 - 6) `rArr` w = 12 + 9 = 21 joule
II format: (when F is given as a function of x,y,z)
if `vec(F) = F_(x) hat(i) + F_(y) hat(j) + F_(z) hat(k)`
Then
`dw = (F_(x) hat(i) + F_(y) hat(j) + F_(z) hat(k)). (dx hat(i) + dy hat(j) + dz hat(k))`
`rArr dw = F_(x)dx + F_(y) dy + F_(z) dz`