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3361_soln_quiz1_F2009

3361_soln_quiz1_F2009 - ENGM 3361 Fall 2009 Engineering...

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Unformatted text preview: ENGM 3361 Fall 2009 Engineering Mathematics IV_C Quiz 1 Full Name (Print): ID: B00_~_§_9/{;_M/1flnh//-H Signature: Time: 3:05 pm — 4:55 pm Date: Tuesday September 22nd, 2009 Room: Chapter House 107 Prof: Edward Yao INSTRUCTIONS 1. Show all steps whenever it is applicable. 2. Use reverse sides as scrap paper. 3. All features of sketches must be clearlyjustified. 4. Keep your paper tidy. EXAM RULES I) No questions will be answered on any aspect of the quiz. 2) If a student requests to use a washroom, an invigilator has to accompany the student as he/she leaves the exam room. 3) All Dal student IDs will be strictly checked. 4) Every student must sign on the front page of her/his paper. 5) A student must obtain permission to leave his/her seat. 6) No communication or exchange of information of any kind between students. 7) No scrap paper, calculators, class notes, textbooks, or assignments‘ solutions will be allowed. 8) No students are allowed to have cell phones or any other communication device with them, even ifthey don't use them, and even ifthey are switched off. 9) Possession ofa prohibited item is considered cheating, even if use ofthe item cannot be proved. 10) All bags must be left at the front of the room. I I) If cheating is suspected, the student’s paper and any suspect material will be confiscated, a notation made on the paper, and a new paper provided for the remainder of the examination. No exceptions will be made to the rules for any reason. Any student who does not conform will be ejected from the exam. Questions Points Mark Part I 2 Part II 4 Part III 7 T Part IV 2 Total 15 Part] [2 points] ‘ Ql Show that every angle inscribed in a semicircle is a right angle, as suggested by a figure to the right. Proof As Malta/ml M +Le alcove lt‘fjwe, .3 -> “ . I! \ Cl ““01 b 6‘"? Y‘O‘AAWS VQC-l'ovg W‘H) ’cou‘ls (ill the (0,er of tH Cx‘vle. W-Q weed glam“) Owll/ qupfi a~fi ( TL“? V-QCAvr alOWj 0w{ Y‘cuj 0f 'lLI-Q (Angle) A l-S OY—l-l-mj'owo‘l Jco "a—b (+L4 veH—or “long We mm raj ). In 01L“ vomit, W41. wiSlq ‘ko Show Ham/1‘ (§’§)-t—£«fi)=0 \ ._\. .3 Tim \aSH- egmovh‘aw halal: SHAW 0\ anal lo Owe Va&\‘u$ Veal—WT “HA/4+ have 'HA—L Same lP/V‘S’H’ , “MM/16H) lime Yaolx‘ug ”‘l 'Hq C/Cvcle. X /// Part II [4 points, 1/2 each.] Q2 . Let 5 be a vector in 933 , write three forms of representation of 21. Forml: a= < a., 0\2, (23> fl .——5 .—‘\ .—\ Porm2: a= (1.; +02J +azl< _. A A \ Forn13: a: [Lanai Q°=_.Q_’ if 0+0 ls the speed ofa moving particle a vector? [answer either “Yes” or “No”.] No Draw a position vector 21: < l, l, l> in the following Cartesian system. (sketch all necessary features) Does 22x2) :6 always imply either Z2: 6 or [3:6 ? [answer either “It does" or “It doesn’t”. It doesn’t Let 2, —7, and 5 be intercepts of a plane, respectively, in the x—, y—, and Z- axes, create an equation of the plane below. 75 ,1 l: a+~7+5| Given a space line passing through a point (2, 4, —3) with a direction vector a= <1, 0, 3>, create a symmetric equation ofthe line below. 1’0? : 2+3 ’ iii—J4 Draw the vector (3 — b below. a E \ If 71(1) and 772(1) are differentiable, then -.\ I [mo-ml: “(’Wfi‘t“ EWWE" Part III [7 points, 3.5 each] Q3 1. Find the distance between the following two paralleled lines. Lincl: izflzfl; Line2: x—H:Iy_—1:Z_3 —l 1 1 —l 1 l [A proper graph is requested.] [Hintz Pr ojgg = [931% for non—zero vectors 2i and I5 .] a-a < elm-49M As Show“ \L‘ H“ paw] Ps(°, L4) “68 \~:\ LCM; 1., 4,1,(41‘1 g) Ides l‘; LeHC. a Lint 1 final LL: 2 have H44 4am dew/WM». Veal—or 5:104, l, I; _ .1 — ' Aka, V1m=ofl 'opl—< 0,1, I) < m, 2) A VY" 511‘: LR'fl 07—. "+°—4'<—l, I, l> 0‘ a-a 1+l’t‘l :fi%&-II‘I l) S— »S :5 _§’;‘-/ 3! }> > A A S“ ,f ,3" d‘VvVu’?*°ja‘9"P“<" o, '4.> ~<Tl 3/ 7> “’< 2,1, g) ’7— :— :Z. -—< 713/ 3’ MW..— > 1. L , L nau=jt~§>+®+tlg \ a ‘1 a K :J 7i ”I [email protected] flat. AKA/amok. We Mew» LN»; es 3 MM, 2%? Q3 gotl/Wq‘am 2. Find lim7(f)»Wh6F€ 7(1):<fl, 2’cost, tlnt>. “’0‘ [+2 [CM 1”! __ O—' ’ ,1 Ht)" tn.) '- o+ol ’ Q 0 [Ii/”1+ QCoSt - lcflb) = l {—70 f [um {"H’t‘ :— lum+ 11" —-— 2.2+; - [ts-r {776* {7-70 T; 3C1 o L/HasPH—al’s Quie ‘“ 1 \w Y‘L’c)=<’all 1/ o> + _)‘) Y xx Part IV [2 points] Q4 €0lM/h‘w (i) (ii) Draw a parallelepiped with edges [1,5, and E . Zio(5x5)l=l(iixl;)05 Show that \ ll) (ll) N04,; flmf +La VO/MM 4-fo .5 .3 loam/lexlfiu‘ltk’d w-‘M {43438 a, [0/ A .3 an (bXC)]/fis A ...
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