{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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. ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online