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Unformatted text preview: ENGM 3361 Fall 2009
Engineering Mathematics IV_C Quiz 1 Full Name (Print): ID: B00_~_Â§_9/{;_M/1ï¬‚nh//H Signature: Time: 3:05 pm â€” 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 clearlyjustiï¬ed.
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 assignmentsâ€˜ 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 studentâ€™s paper and any suspect material will be
conï¬scated, 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] â€˜
Ql Show that every angle inscribed in a semicircle
is a right angle, as suggested by a ï¬gure to the right. Proof As Malta/ml M +Le alcove ltâ€˜fjwe, .3 > â€œ . I! \
Cl â€œâ€œ01 b 6â€˜"? Yâ€˜Oâ€˜AAWS VQCl'ovg Wâ€˜H) â€™couâ€˜ls (ill the (0,er of tH Cxâ€˜vle. WQ weed glamâ€œ) Owll/ qupï¬ a~ï¬ ( TLâ€œ?
VQCAvr alOWj 0w{ Yâ€˜cuj 0f 'lLIQ (Angle) A lS OYâ€”llmj'owoâ€˜l Jco "aâ€”b (+L4 veHâ€”or
â€œlong We mm raj ). In 01Lâ€œ vomit, W41. wiSlq â€˜ko Show Ham/1â€˜
(Â§â€™Â§)tâ€”Â£Â«ï¬)=0 \ ._\. .3
Tim \aSH egmovhâ€˜aw halal: SHAW 0\ anal lo Owe Va&\â€˜u$ Vealâ€”WT â€œHA/4+ have 'HAâ€”L Same
lP/Vâ€˜Sâ€™Hâ€™ , â€œMM/16H) lime Yaolxâ€˜ug â€â€˜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> ï¬‚ .â€”â€”5 .â€”â€˜\ .â€”\
Porm2: a= (1.; +02J +azl< _. A A \
Forn13: a: [Lanai QÂ°=_.Q_â€™ if 0+0
ls the speed ofa moving particle a vector? [answer either â€œYesâ€ or â€œNoâ€.] 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 â€œIt does"
or â€œIt doesnâ€™tâ€. It doesnâ€™t Let 2, â€”7, and 5 be intercepts of a plane, respectively, in the xâ€”, yâ€”, 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, â€”3) with a direction vector
a= <1, 0, 3>, create a symmetric equation ofthe line below. 1â€™0? : 2+3 â€™ iiiâ€”J4 Draw the vector (3 â€” b below. a E \
If 71(1) and 772(1) are differentiable, then .\ I [moml: â€œ(â€™Wï¬â€˜tâ€œ EWWE" Part III [7 points, 3.5 each] Q3 1. Find the distance between the following two paralleled lines.
Lincl: izï¬‚zï¬‚; Line2: xâ€”H:Iy_â€”1:Z_3
â€”l 1 1 â€”l 1 l [A proper graph is requested.] [Hintz Pr ojgg = [931% for nonâ€”zero vectors 2i and I5 .] aa < elm49M As Showâ€œ \Lâ€˜ Hâ€œ paw]
Ps(Â°, L4) â€œ68 \~:\ LCM; 1.,
4,1,(41â€˜1 g) Ides lâ€˜; LeHC. a Lint 1 ï¬nal LL: 2 have H44 4am dew/WMÂ». Vealâ€”or 5:104, l, I; _ .1 â€” '
Aka, V1m=oï¬‚ 'oplâ€”< 0,1, I) < m, 2) A
VY" 511â€˜: LR'ï¬‚ 07â€”. "+Â°â€”4'<â€”l, I, l>
0â€˜ aa 1+lâ€™tâ€˜l
:ï¬%&IIâ€˜I l)
Sâ€” Â»S :5
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> A A Sâ€œ ,f ,3"
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â€œâ€™< 2,1, g)
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nau=jt~Â§>+Â®+tlg
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[email protected] flat. AKA/amok. We MewÂ» LNÂ»; es 3 MM, 2%? Q3 gotl/Wqâ€˜am 2. Find lim7(f)Â»Wh6Fâ‚¬ 7(1):<ï¬‚, 2â€™cost, tlnt>.
â€œâ€™0â€˜ [+2
[CM 1â€! __ Oâ€”' â€™ ,1
Ht)" tn.) ' o+ol â€™ Q
0
[Ii/â€1+ QCoSt  lcï¬‚b) = l
{â€”70
f
[um {"Hâ€™tâ€˜ :â€” lum+ 11" â€”â€” 2.2+;  [tsr
{776* {770 T; 3C1 o
L/HasPHâ€”alâ€™s Quie
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\w Yâ€˜Lâ€™c)=<â€™all 1/ o>
+
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Y xx Part IV [2 points] Q4 â‚¬0lM/hâ€˜w (i)
(ii) Draw a parallelepiped with edges [1,5, and E . Zio(5x5)l=l(iixl;)05 Show that \ ll) (ll) N04,; ï¬‚mf +La VO/MM 4fo .5 .3 loam/lexlï¬uâ€˜ltkâ€™d wâ€˜M {43438 a, [0/ A .3
an (bXC)]/ï¬s
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 Fall '09
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