Question

curl(V) = 7*V = (01,02,03)X(V1,V2,V3) := ei(@2v3 —@3V2)+e2(@3v1 –O1v3)+e3(@iv2-02vi) for any vectorfield V = viei + v2e2 + v3e3 on R.

Answer 1

Ans Given that for any rector freed v=vie, the 2 +V283 -1), we have curacv) = 0,Cap 13 - az vz) tezlazmy - 0172) +63 Care-azri). Nel reicām"3 - Sa. 2) +ez ( Santos - Sa, 27+ez (Bax, x2 - Bxr7 so for v= 1793 e, th, 93@2+,9263 - we have read213 , 2 =21813 and 13=1182. Nowe curd CV)=e, @, v3 - Bazve) tez (@azri - BX, M3) 1 +232 x 2 - 8d2") = el labas, (142) – Əng (4193) +67 @ay (17 243) - Sa Pires teslam, (8183) - Ox, (2293)) =01(21-21) +7 (92n42) +e393-83) => curl (1) = oe, toe2t003. CANS) Given that m= 293 2, + 5%, Cat 41203 · compaining with ean (I), we get Ni=223, 22=5*, 3=482 so conecmaer contro ter and tezo ) Bei (, C4 xs) - Sq,45*))+ez Cam, 192)-Bak 4 tes (,15) - ACP93)) = 01(4-0) tezc2-0) +63(5-0) = 48, +222 +503 Cans).

4 Given thad A= alitbetrez- => 3 A = 3 Cae, the treg) =) = 0+1 + $ 2. - Now $ xx = ce either Given that A = ae, they +(@3. = $ = { cae, they tres) = 90+kezt fes Now @xx = ente2 + 3) x (x2017 21282 +63(3) =>= 3 xv = l ei a ezi al bl2 l2 11 12 13 = arc *93 - $ *42) - ez (9/2*22-472821) tes (42 m2 - 612.91) >> V = eicams - Š x2) - Oz (2013 - $ 9)) te3cfa2-91). so cuader) = 10 Sng Cahay - 91) - Song (-$43+ $91] + , 3) - %, (332 - 3 ) tez [, (- 2 2 2 2 2 2 2 21) - 89 m2 (2 93- {{22)] 2011-0)-(-4 +0] +ez[(-o)-10-)] tez [cord)-(0-{n} 5) Cuod cr) = (24) +62 (22)+63 (3)=&tbez te is