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# 4 - Problem 2.1 By evaluating the dot pmduut U-V prove[he...

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Unformatted text preview: Problem 2.1% By evaluating the dot pmduut U-V. prove [he identity unsiﬁl —61]= L11SH|cmﬁl +sin9| sinﬂg. Strategy: Evaluule the dot product both by using Eq‘ (2.13) and by using Eq. [2.23]. Soiutilm: Tin.- slrutugy is to use mu dcnniL'nm EL]. Lilli} :mLI 1|": El'. 11.221}r Fmrn Eq. {2.18} mid IJJL' ﬁgure. 1f - V = LUIIVICGHIHI — £13}. From Eu. (2.13} and [he ligurc. U = [Uitimsﬂ'l +1 sln Ha}. V 2 Wlﬂuasﬂg +jsin ":1. mad the ilnl product is U - v = IUIEVHL‘DW: mm; + sinﬂ. sinﬁ'ﬂ— Equaling IhL' lwo resulLs: H- V = illlWlﬂEE91 .. Hg] # IUIIVHELBUE urns-El: + sinﬂl sill-‘11]. ﬁrm: which if |U| a! I] and W1 ié LL '1: follows Ilwl Q.E.l}. mam. -H1} = c0511: chsﬂ; + sinﬂl s‘mﬂg , Problem 2.118 [11 Problem 2.1]?,determine 1h: veclur compunent of T normal to ﬂu: bar CD. Sulutiﬂn: me E’mhﬂcm 2.11? w: haw.- T 2: {—33.7i + 3E1Jj+ 333ch N Tr. = {3.4m +5.”; ., 429k} N TI": "mum campuncnt is [hen 1'" .__ 'r .- 1',, Tu =(w311i + 3] Juli + 3.22%.] N H v 0.5 m ...
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