MAC2313_Test1_Spring2010_Solutions

# MAC2313_Test1_Spring2010_Solutions - Page 1 of 4 MAC 2313...

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Unformatted text preview: Page 1 of 4 MAC 2313 Name i<€=§‘ Test 1 Date: January 21, 2010 Clearly show all work for full credit. 1. (6 points) Find an equation of a sphere if one of its diameters has endpoints (2,1,4) P and (4,3,10).Q Cami-er: C: AJJPDME 0F 13 g Q 2 (3) 357» r: «mm 1‘ I591”: } [94-1313 *2 J11 6-3): + (76\$? + ("2x712 H 2. (6 points each) Given points P(1 ,-3,-2), Q(6,—2,—5), and R(2,0,—4) in R3, (a) determine whether APQR is a right triangle. :2: Hindi, I r3> (b) determine the area of APQR . 14mg op APQR : 15W71W71=§ 1M+~¢1m~l+g Page 2 of 4 3. (3 points each) Given a = 3 j — 4k and b = 2i — 2 j + k , compute each of the following: (a) (b) (C) (d) (6) (f) r1(t)=<t,t2,t3> c<o,3pkt> .. 3b—Za lal'zm =5 =<a,~a,s7 .. .. 7~7 '7“! - 351843018 49:4 «8c r03 34, : 0404i: «~10 “P «7 .2 *‘? “:7 axb " ‘5 k L J O 3 —L{ O 3 :2 a l 3’ ‘3 2 Z? X “g: : <-S ~8,~é> the angle 6 betweenaandb .7 w ‘9‘“ 1235““ “ 5‘3 ‘ 3 -9 4‘9: (105% (“A a unit vector in the direction of b “j “#7 a 2 -3 ‘L U :‘lﬁ‘b 2 Jj<9, 9,\7: < 3) 3) 53> and my? .... .. ,~> “Si? -83) _.(ok- (El: d‘l+‘-l+l t 3 r2(t) =< 1+2t, 1+6t, 1+14t> 1: "v (8 points) Suppose the trajectories of two particles are given by the vector functions for t> O. % Determine whether the particles collide and, if so, the point at which the collision OCCUI’S. 31¢ tLe pit/triﬂe; 'Kr—X 13-: Hal: :5 11::‘4 gown“ am g NO 5 pica 5 > 0 TL». Pct/#1171» J0 ml: (gaggle, 42,-e,3>~— <0,é2;~8> : 4c,«Ia)II> ~7 Page 3 of 4 5. (8 points) Determine the point(s) at which the curve r(t) = < sin(t), cos(t), t > intersects thespherex2+y2+22=5 ’X "I E :1 ~ ‘ + «\$479+ \$4 :> safes) + «teach 139:5?» 1+6 :57 => 15 ~ ~07 1L5 WM [Alexa/£5 [1c 5PM wt P< 5am, (95(9)) 93 not (3 (5M (“‘93, Cos (‘33) “23 6. (8 points) Determine symmetric eguations for the line in R3 through the points P(6,1,-3) and Q(2,4,5). a”: p79 2 wreak-M Veal/Dr v”: Ange» Wtha PCB} ’l’3) ) __ .4 2+3 7‘ (0 ~ 1-3 1* T :~ 7. (8 points) Find an equation of the plane through the point (-1,6,-5) and parallel to the planex+y+z+2=0. Le angmv Paw, m "a : <~ w x+v+2 :O 8. (8 points) Find parametric equations of the line of intersection of the planes 3x—2y+z= l and2x+y—32=3. 39c »- an + z : l (9x+’v ~3EZ3 BM; 71‘ -* 52 ’1 7 IX: l 2) '5: 0 2» PVT“ :>P(l) l) 0} L18 64 £142. Evie, IX: 6 :1) z 1 7 :11) (V: i; 2) (.9 ((0) la) 73 [5’ O" [:11 ﬁﬂi-e, {7): F6 “T: 4 5)“)fi7 :- plwta/itm Vex/{Dr Mmg PU, MA or: HSt “I“: Hill: 2: 7t Page 4 of 4 9. (8 points) Determine whether the lines L1 and L2 given below are parallel, skew, or intersecting. If they are intersecting, ﬁnd the point of intersection. .. _. "f, _ .7 L11x+2=y1=z 2 V‘ZZ‘MQJ» EVFFKV; 19w Mia‘k 2 . L - x‘3=y_—2=Z- any»; a) :7 L- n M; meﬂej to L 2' -4 —3 2 9 5 use. (E as Fan/«weer tea/L S as Pcu’wkaéef / Lhzvf: 5 ‘45. . _ 35- :5 Q: 3 ‘ls L‘— X‘: (3-; V: ”at 2 2+ 2:: »;+’:2t;‘ 1.? 35 L31 “X: 3—45 «1-: 2~3§ 2 = [+215 2+Et: H25 —~ ~ - :1: Mala TL get: Macs «53 a 33 >H\$s=a 35 75 S 18 U Wt t— *9 a 8‘1”“) {J‘ﬂ Pm ”I: (“LL 22) “3 L‘) L! (0\ On L4} null: age Scale in} :L h 1 Ac 1% see a S: (8 (ﬁn/“(.43 {’Lg Pcmt (L! Q) 03L“ L‘. (a) 0“ LR r: L, 5 If: L. j’f—a 5km SKEW 10. (8 points) Find an equation of the plane that passes through the point (1,2,3) and contains the linex=3t,y=1+t,z=2—t. P093) t=O :7 QL0M3\ Om {La [he ‘ A 4-. 5&AQL3 53*: 3C; zé’l)“l,‘l7 }& A0,,ml vex/kor‘ £9 a I c {a (L ‘ : V 3 i i %m& (arr-a, I) ant/k £47 of ﬁg. FQMES P’Q’GK R) i’X‘pr‘Z Oi ll. (8 points) Find the distance from the point (—6,3,5) to the plane x - 2y — 42 = 10. , { [5| Aig‘Q/(jllD/‘x Vac/{or QK a [We FC/Pﬁarjrlkﬂf 14:; {LL (91mm LS <l {3,40 ’ L ' x- *é'l- t \11: 3— Qé Z : 5‘ L164 (:5 lie. gran“ ﬂ/U‘vL‘ PL‘G,3,§\ {Lat i: FQ/Pﬂtd«d\&»€@’ (:7: as Plano (ﬂax: («Half ’ A y P p {L¢ [vie Wig/2w (LL [tn/€444. is {awn} E7 716 loll/(RS anti; on O («42%) - 22634.29 ~— Ll (54L: Q - (o; Soft/587‘; ...
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