Question

Calculate [rı(t) r2(0)] and — [rı(t) x r2(0)] first by differentiating the product directly and then by applying the following formulas: dt dri dr2 [ri(t) r2(0)] = r1(t). dt dt + . r2(t) dt dr2 [ri(t) x r2(t)]=rit) x dt + dri Xr2(t) dt ri(t) ) = cos ti+ sin tj + 5tk, r2(t) = 4i+ tk Enter the vector i as 7, the vector jas į , and the vector k as R. [rı(t) · r2(0)] = ? Edit (ri(t) x r2(0] = Edit dt

Answer 1

given that n H = cost + sint that a TH) =iitta Now To Ho H) (cost 7' toiatū +678). 197++) 4 arst tat Now & [PH. KHI = [gcost tát"]= (400st)+(at) -4 sint + 10€ therettore shih). Tih)] = Hot - Asint

NOW von Inits ūHi] + my (4) dt ñHl. añ dt dt =loust i+sintitāti. (vttás + Lustitsint tatil). (17 toth =( costitsintot rath ) (#14)) ) +#70044) 7 + #lint)5+#157. (7+ta) =l cost +8Httatā, (0.7+lW) +3 (-sint; 7'+(604)j + Doty. (T+ ta) [it ata 149234 934 (5+) + (4) 4-sint) +50 40t - 4 sint Hot Asint therefore in Hin't? T= hhehh 9.b = a16492 6279363

Now ritt) on 'HI i j K sint cost 4 t S A It sint); - les t-204)j + (-4 sintjü Now & [rix r [ht sjutti- /toost -20t)+ tasjnt) ū] #ftsintji - at Heast-204)5+ at 4-25int) i ft & Fiat )+ out #ty ztcastle 't f costat) 30##) & -4 sint) T Htoast + sixty 7 - {tsintytt)toest-20 young - cost a (sintetlosti + (tsint --Oost +20) j - Youst therefore o n'It)(4)] (sintttasti + (tsint, cust+2015—qaustü S

Now Ini H) X H) P Hồx 96. at an XhH) dt =(costi + sint 5 that ') x (17'étā) +#casti'+ontj+rath Jx(47'tH) Now, = bit habah = costitointi+ata )x(0+17) + (-siut it awtī+ 5ā DX (47+th) (1) ousti+Guti't tax ( RE=97427497 it then RXTO= Qust sint at 93 O {(siunt)0) – 057 cost-0) torty sint? - cost and f-sint T +08457an Jx1474 +ū) = 7 J 91 o bi bz 0 1 i j - sint cost 1 0 t toost)-(-tSt-av id east) k = +008t; + Itsin ++20): - 16ost

therefore from (1) he get (trust it gint J+57ū) x (# )+1-8int 7+ cost +55 7X (4th = sinti- cust. + toust it + Sint +20 jj – 400st ñ = (siut+toosty + Hsint+20-cost}j - Aoust ū therefore, at Ereix Pit] i sint tteost) it Hatut+20-cast) ja -alusta