Question

Results for this submission Answer Preview Result Entered incorrect incorrect incorrect 3 of the questions remain unanswered. (1 point) Find the work done by F along different paths between (1,0, 1) and (1,1,0) You might simplify your computation by writing F vector field G + H = Vg + H, so that you have a decomposition of F into a conservative vector field and a simpler non-conservative F (ez y, xze +z cos(y) - 3z, xye2 + sin(y) + 2x) (a) The path is the straight line path between those two points. Work is (b) The path consists of the line segment from (1, 0, 1) to the origin, followed by the line segment from the origin to (1,1,0). Work is horizontal segment to the origin, (ii) the parabolic path y = x2 from the origin to the final point. (c) The path consists of three parts: (i) the vertical segment down to (1,0,0), (i) Work is Note: You can earn partial credit on this problem. Preview My Answers Submit Answers

Answer 1

sol : the given function is Far4zty, 22%2+2 cos (4) -32 , xy&%2+ sinky)+21) fa reyz , aze42+2 costy) , 24e9?+sinly)>+4,-32,21) F = 09+H They -32% +21 7 the path is straight line between (1,0,1) & (1110) - (a) 2-% 2-1 y-0 Real = 75't 1=1, yat= 23-t+ rię tyotol fe=o . fo = ct , f₂=-dt work done was fudr = f'(vg+#) dr - Sog det fudk • Hidr work done W. ( tro Cs Scanned with S tg + s (og fx – 32 ły +2x fz) Scanned with

2 991)-960) + ſ (y c01 -32 (04) +2x pd t) tit) where 9=e +Cr-t sint 9(1) s e'to sink = || 9 Coseti sinca ! 20 - + = 1-1 tf 10.-3 (++1) of +0] 70+ Ś (34-3) dk = +(34)' 1962), -3(1-0) = +3 -301 (6) cacing where all the straight line from Cleopp) toloro,ch s ayo?!=+ 2.-++ ,4-0,2=++ is to fx = -dr, fy=0 f = -dt gitla-r+ 910 -0+1=1 901 -1+1=0 work done w a I Fdr = (09+H) dr - jog. dr + 9 'Har +961-967 t s ro fix =j2 by +20 fz) rs Scanned with CamScanner

50-1 +S-469) *J (+++1169 +2 6+4 +1) (-dt)? = -1+ s (21- 347 3re3 F24 tahdr arettedr -0 1-2 - -2 2-1 + (o=-2] (01010) to (1,1,0) over a: a is a straight line from nar, yarn 20 tua dr , tj adr 9 h = 0 is total Spor = 569+1) dr - fredet førte «-sely infe) =9in-g(a+sy dr- -3 (c) di- t2t (o) ] dr O g (tla teple at 91111 , 9(920 kot yat 31+123=14! citle= -2 + 12 = 7 Word done ( work done is we sadr G illar) to (110 162 (1107c) to (0,0,0) Yzx Coropol to clillo) wa Hdr = rs CS Scanned with work done TW = -5 CamScanner