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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 Camier: C: AJJPDME 0F 13 g Q 2 (3) 357»
r: «mm 1‘ I591”: } [941313 *2 J11 63): + (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“! 
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O 3 —L{ O 3 :2 a l 3’ ‘3 2 Z? X “g: : <S ~8,~é> the angle 6 betweenaandb .7
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“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 ~ ‘ +
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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 wreakM Veal/Dr v”: Ange»
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7‘ (0 ~ 13 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.
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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 ﬁﬂie, {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
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L‘— X‘: (3; V: ”at 2 2+ 2:: »;+’:2t;‘ 1.? 35 L31 “X: 3—45 «1: 2~3§ 2 = [+215 2+Et: H25
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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
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i i %m& (arra, 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. , {
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 Spring '08
 Paris
 Calculus

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