MTH203fall05 (Exam 1) - American University of Sharjah...

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Unformatted text preview: American University of Sharjah Department of Computer Scien'ce, Mathematics, and Statistics MTH 203 - Exam I September 29, 2005 Name: ID# Section: Q1.(20%) Given the points P(l, 1,1), Q(l, 150) and R(l,0, 0). Find: a) A unit orthogonal vector to the plane determined determined by P, Q,andR. z<53,1‘9"‘> - P? 9' 4 0”” Fl) _’ a K x V N: pbeR—Nto c: \: <,\/0)o> a 'l " 5 A -.= 44,010) b) Parametric equations for the line through P that is parallel to the line through Q and R. -—— ' (9?; z < a, 4, o> \ ’4 I I 5 R 7: 3 Z l («k NW C) The area of triangle PQR J'— 9 V5“ 5 2. W d) The distance from R to the line through P and Q. Q ? a; Male/M [Pill ' Q2 (12%) Show the fqllowing two planes are parallel and find the distance between them: 2x=4z—3y+4andx=22—%y+3. ' m) {ll zx—H?+39’Ll 18%” <Q’JU?) {352%, I x WWW/12>. WM. it #7 kg plqu M Q3.(14%) a)Find the parametric equations for the line of intersection of the planes 2x — z = 1 and x + y — z = 2.Find the angle between the twoplanes ’ igfb 2%; I+f~ 2))61” Lg . ’2’}? :— é’.%/%+L g V 92’ W 3 . ' sir-3h t MHZ, 7’ . Z 7; 4.7/3? “Y Vb N‘ / 42lo)'—l> f‘ if % (il‘/’l> ’ 7f/ N2 Q .NL ” / 7' J @369) “MIA/1| ‘ 1a (6%) b) Find an equation of the plane through P(4, 1, 2) that has the same yz-trace as the plane 2x + 3y — 42 = 11. 2 wwrt WNW! A [X»H)TB/0“’)+C{P—2):o it Ax/rb’tg'rt €2¢¢M+8+2€ Tm trace “’7 n 1 39M? 1—th «#574220 1; ii SIM 3;?) r’@ 'aMW/WM ' Vt C;’,// H! / 5“ / 4 \>/\\)C\\@] ‘ié WV (:4. (20%) Let f(x, y) afflflii if (x, y) at (0,0), f(0,0) =0 2 2 x +y a) Is f(X, y) continuous at (0,0)? Justify your answer? } Iv? 3 f f 7 ‘ I gag; SA, 3 M X' r: O b 70/ fl ’3? 5 x60 ' M ,xgax3,t7(3'>() : 3 ‘7 3 '3 K: ‘0/ 60' W 3 W3w9{9}sm(w 4’ ( Camilqgo $106 at (ma/tin)!” 2 W a”), 3 ., ( 5/ , :M WEC‘VO) w 0) 6 V60 ;: 'P/OIO) _ (I ,4" C) - I {gag/gird M 7Z5}! *4 M20) b) Does fx (0,0) and fy(o,0) éxist? Justify your answer? ' o W )3, ' flow) $2 AW,” gj’f‘ I i X >Ax__bo DX - A)an Q5.( 10%) a)If z=f(x,y) is implicitly defined by yz +xcos(z) = 1+22, find if (:zm,?):loz+xwé)~%?~l=o 0y M“ 21:_F fl_ F2— — gr—X.5’n;fl?z «9 &;P§FFH ,DX {27 ” 945mm,? b)(10%) Use the chain rule to find 135% if w = r2+sv + t3 with r = x2+y2+zz, s = xyz, v = xey,t = yzz. mgayafi Q—Ligiak—M ’D’t awgnc* 3/ {AM // O L2 intersection. W Q6.(12%) Determine Whether the lines: L. :x = 2—t,y = 3t,z ='1+t,—oo'<t< 00, and :x= 5+2s,y=1—s,z=8+3s, —oo<s<oo, > are parallel , interSect or skew. If they intersect, find the point of /—'> 62 6 4'\)39'> ’9. £72 C b 0\ mi Dada/“'73 (MIC 0‘ X _g 2AM ’7 2"{15'1‘75 Subgllfih@ z: I'— r. 7/ L ‘ 5;“ M51353 1M” Spf-7/ 9AM +5 Ml" g/é (/1 w W l m a) % VOW, ((zvzit’éc / ...
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MTH203fall05 (Exam 1) - American University of Sharjah...

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