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integrate along the path F.dr
Don't you need to Integrate?
how would you do it when the path is a straight line?
give us the question..well see
between point (3,0,0) to point (0,pi/2,3)
when the path between those two points is a straight line
I'm having trouble knowing what to do when it's path dependent.
whats the force?
F(x,y,z)= z i + x j + y k
so dr is the distance between the two points?
first write the eqn of a line in cartesian form like x=3+3k y=k(pi)/2 z=3k
parametric representation of the line segment right?
the work done is F.dr which is
sorry write y=-k(pi)/2 and z = -3k
got it till here??
Kinda it's just hard to remember how to find the parametric equations of a line
no bt ive written em down fr u nw
kk so use dot product of the vector with dr right?
so you just replace x y z with the parametric equations right?
so here goes dot prod gives zdx + xdy + ydz for zdx write (-3k)(dx) (-3k)(3dk)
now integrate this -9k^2 dk from k =0 to k=-1
coz k=-1 gives u ur final point
now similarly compute it for xdy and ydz and then add all three/
Yes so my area of integration is going to change because I reperamatize right?
yes integrate all three frm 0 to -1
bcoz remmbr on ur line k=0 gives the initial pt and k=-1 givs d final pt...so as our integrating variable is k, we use the lim its fr k
that should do it i spose
yup my book shows it but in two dimensions....
js get the answer and tally it..its complicated enough...ur book mightve represented it in 2d..fr me dis is d way i thot dis cld be done
nothing I got the answer