2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...

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Question

Answer 1

Answer #1

1a. F = xî + yſ + 2zŘ S:z = x2 + y2, z si A vector normal to the surface S is = (z - x2 - y2) = -2xî – 2yj+k and the unit nor

F.ñ=- -2x2 – 2y2 + 2(x2 + y2) (4x2 + 4y2 + 1) (14x2 + 4y2 + 1) = ° As F.ñ = 0, thus SF.ds = [] Fºnds = 0 F = zî + (x – z)j +

= V(1 – x- y, z) = -î - ſ-k and the unit normal to the surface is given by - –î li ħ –î lî - Ŕ ** (11+1+1) (V3) -i-j-k (-z-

(0, 0, 1) after proection on xy=plane (0,1) N =1-x 0 (0, 1, 0) y=0 (1,0) x (1,0,0) x=0 y=0 jer-as= 1) (-345- | | 1 | Teledy -

- - (+) - - / (༥1 -) + –༧)de -- - / (s=༧) + 0 =)) as = -( * d=༧) ༼/ 111 6 - 2+ 1 +- ༡

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Answer 2

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