Question

Let Ě = < 2x + y², 8y + z2, 6z + x2 >. Use Stokes' Theorem to evaluate so F. dri where C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1), oriented counterclockwise as viewed from above.

Answer 1

G 8 2uty 2) i + (8y+2); (62+x2 k Stokes theorm SP 7. dz = SS curl?. ds Cwel ? C. K d ди dy (anty2) (8y+22) (62 +22) 12 (62+x2) - oy K [ 3 (3y +22) (6712) 3 C*+2>] -- [3 (2+2) (2013) o y Contyd) tk i (-22) -j (2n) - K (24) N - 22 i-on j - 2y k Points are P=(1,0,0) Q=(0,1,0) Rz 10,0,1) then two vectors that must lie the are blane Q 8 (1,-1,0) Q R 2 (0,-1,1) Cross product QP x Q :(-1) -j (1) +k(-1) z-i-j-k

Now we can use any the point in af owe point. one equestion Welde use Q for The equation of plane is - 1 (2-0) - 1 (4-1)-1 (2-0) = 0 - x - y +1 -2 zo h-x-l az fra, 9, 2)2 Z+xty-1 ja o llfall <,',I> Curl P. 51 (-22 i - anj-2yk) (i tjtk) 13 N - 2 (1+y +2) 111) e P. dr SS curls as N is (-2(uty+z)) da SS Tofu put h-x-1-2 TSSE -2 (1) d A llfall - 2 TSS dA N S llfall

С 1 - - - همراه جم TX E- - [ e, e n-no up (n-1) (1) [y] up b = dy da x-1 S s curl?. de EPI l=htu 「ライラ。 x-1 h = a 1-htu ny blane 6ں
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