sol3 - Math 2163 Jeff Mermin’s sections, Quiz 3,...

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Unformatted text preview: Math 2163 Jeff Mermin’s sections, Quiz 3, September 15 S o l U‘l’ions - 1. (2 points each) Indicate whether the following statements are true or false. (“’I‘rue” means “Always true”, “false” means “sometimes false” or “possibly false”.) No justification is necessary. Write out the whole word “true” or “false”. A, B, C, D1, and D2 are numbers, and :c, y, z, s, and t are variables. A7 B, and C are not all equal to zero. (a) The equations as = 27 y = —1, z = 0 define a line. g 0) 0+5“ 5 S‘l‘ch/s LowrimO (‘5'. 7 Tabb, +0“) (about; cos“ C(Qo.\vQ, 0x lx‘lur, WM m M Plomis Mittoéxocw} alum l'lu. vht‘rclx mYoSl . \1. Mile no 302xng c, pol/VT» (b) The angle between two planes is equal to the angle between their normal vectors. \. SOl0+l0n L7 "Rid? ROS-5‘ ' Tme a 70H 'm fixéhookz "If We elm; ‘1) a it not aandlti. Hm. iv“, mama m «x Sh'uizflfi . I ‘ ‘i-M an! H‘ may bdwm “4 “w glans .3 {it-qul as J M acuH, MWJU' “Mich «mix mrwal Vic-bf; " (c) The lines (x, y, z) = (—2.3, 2)+<3, 4, —4) t and (my, 2) = (—53, —1, —4 — 3s) intersect at the point (—5, —1, 6 . ) Sol V4700 Jus‘l'ync NCMQ‘H'): If 'Z+3t=-€= 0 t=~i zj—z—az—rs 3) 2-4H)=”t-ECL 34425: -—1 ~ 5;! Co:_..} 3) Z ~4t= 4"3 5 FQlZ, Sow-"’5 4:3? 5 and}: Er 4:; “first flaw ééaaé'.””3 8"“?! // emf/S’l/Zué flies! do not SEHEQ m Mm! agrarian] \\ é (d) The distance between the l ‘ panesF.A2:+B +C' =D ' Ax+By+Cz=D2ile1—D y Z landG' v 2’. Sol0+lon "Holden Caulgielal”: FalSG becmxse W distcmu is, i “3‘ ' D’Ll KA .B\L>l (6) Two lines define a plane. §Olu+Ion Zack E4467”: mkc, Twu Mags [um SON-6%“ dfl‘fne q {flan Pvt Jr'nfj pug {xx/mm! 07 \Memegk 5d lines we bf gkey/ wwh {Zlfl mew or WW “4:7 do m4 RH'm ex 9 m. /. 2. (4 points) Find the distance between the point (—5, —4, —5) and the line my,” = (_5t,2 + 2t,1 — 3t). {6" b Ja)<g éo\0+ r 6/: ‘ \‘n (4/ £71.13: {9 ' (flqifl/J’fl/X’Oé 4’4” but; ’3’ *6/45) M r i) (M 1.71: ,4 ~44? 7"“ 306.,>—(,-%)<.’—c>){ —‘- 4mg) Jet/‘7) + " “€(wé)r(aé‘ 3" '7 ’3‘??? HI?) “3‘9 ‘4 g. :3; 7/373 3. (3 points) Find an equation of the plane containin ' g the pomts 4, 5, —3 , (—2,2,1), and (—4,5,—5). ( ) Sciatica £7 Chris-Hm 9456/: X points) Find an equation of the plane containing the points (4, 5, —3), 2,2, 1), and (—4, 5, —5). ‘j ’2 _,i\xi2¢<e’OI%Z/nvorz%> 3. (3 (_ 91%,g) ’27 "g (a <(fl/ ’Llfll "' WM) ~ 515M343 7462+ an; {gww’vi’”(4fl *210 r21h2~72:' a 1.- m ~- W ' We 2 w m J 4. (3 points) Do the planes 2m+y+z = —2 and 2a: — y—22 = —4 intersect? If they do, find equations (in one of the standard forms) for the line of intersection. If they don’t, find the distance between them. Solua’len L645: N,:j,)i N,XM,~ ; \I ’T /i I\_ 2! 2w Ni; 3~ifa l-I'Q/ “#1 9‘2 LA~Q 'Nvfiiv‘: 7 / 1+1“) —(-\1—2) 4. (ax—a) o ‘01“ W" a —r —— ‘4 (g'~ {A RFC) " 2., «2 Q) -3, ,. A m a a mu "gi322” ‘93.;9 () W) X _ 3*3 M. 2—4; ; Extra Credit (3 points): The centroid of a triangle is defined to be the point Where all three medians meet. (A median is the line connecting a vertex to the midpoint of the opposite side.) Prove that every triangle has a centroid, and find the ratio between the length of a median and the distance from the centroid to the corresponding vertex. My $olol‘l0n.‘ Lel’ ‘l’lat l’riawfilb Haw. VCr'l‘.’cc$ P; Q, owl R. Then “w Warml’ 0; ‘l’lwe orFosi'l‘c glues OLQ ’K‘l' R R an a c ‘Vcl @f) Elf ) r65? 1 Tl-ws +3“ 61‘)“ "m; a; 'Hfle MCAi'cms. Mr"- <w+>= Pr [Ce—Pie, "av We <2 {be ms, ml MK; “my. R+£Zin-R]U. The“. \ines in+€r$co+a+ 'l‘lw Fowl Prim) 2. when $=t=u 1"; . Thu) FfQ'l‘R [5 +4“ Cen’l-(‘m‘d o'F' +rianj\c PQR) 3 p . and fa qut'fwlqr ‘Hac cen‘l'rotA {Xls‘l‘5. r ‘ ‘ = Crag. 59), OSLOL MCA,’q-n )6 HC Aisling: gram :D+e)‘ F) I J. + La 3,”), A4): centroid +4: +4“ Gaffes?!” In) a. 5&0 ‘ dfs‘lc‘me gram» t: % 7"0 4:: 0. (“=5ch NC l); at“) 3 dam), Mae («HO 1‘" ivcsl‘fan i} (lo—\DICl-qi-o“ : .5 2. 3:2. ...
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This note was uploaded on 10/11/2011 for the course MATH 2163 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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sol3 - Math 2163 Jeff Mermin’s sections, Quiz 3,...

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