223_Exam1

# 223_Exam1 - SQLUTWM3 MATH 223 SECTION 12 FALL 2009 ‘ EXAM...

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Unformatted text preview: SQLUTWM3 MATH 223 SECTION 12 - FALL 2009 ‘- EXAM 1 Wednesday, September 16th, 2009 Name You must Show all of your work in a clear form to receive credit. The use of calculators is prohibited. 1. Find the unit vector from the point P = (1,3,1) to the point Q = (2,0,1). [10 points] ‘[email protected]== E~%§. e) u§eiziﬁ4a2=rﬁ3 : via—24 ether (,1 " ,~_. .._‘_. f , ' '7“\ gv‘ Y . [WWI EB (' 33 2. (a) Find an equation of the plane that passes through the point (1,0 2 and has normal vector orthogonal to both 12’ = 25+ k and 17‘ 7 =i’— 7. 12 oints ‘ K, :- ,. J I P ] K 3 K __, ~_ .2 __; r a ‘ __ ~75 » T. i. K V\ :: {A X , t Z . h, g ‘1 3 2 ~ ' \ ~\ 0 , . 2 . MATH 223 SECTION 12 - FALL 2009 - EXAM 1 (b) Determine whether the plane a: + 3g + z = 7 is perpendicular to the plane —5m + y + 22 = 1. [10 points] VLDS‘WLAX ”Czar (xylem l: "Va :3 H: +33. 4. l; ”MA x3“ elm 11 Iz**ST-*§¢ZE .2 no “\‘K1 2 "S‘V’ED‘TZ: O was)“ l/l/m‘ Nb YUM; mlwv 3. Decide if each statement below is true or false. If the statement is false, explain why (brieﬂy — just one sentence is OK) and/ or ﬁx the mistake. [6 points each] (a) If (i 75 6, then __‘;‘__ is a unit vector. “all ’T—CUQJ (b) Contours of f (a), y) = 3x + 2y are lines with slope 3. the, 9= <1 -* 3M2‘Itc \$1“ ”3:; (we, lit/Raﬁ. “\W 40% ”E (c) The graph of the surface :52 + 22 = 4 is a cone. Reva, \ «'3» L73 a C} (‘tLulAf C31\\ «At? ’5 2X4 Q 2 MATH 223 SECTION 12 — FALL 2009 — EXAM 1 3 4. A boat is heading due east at 25 mi/ hr (relative to the water). The water current is moving toward the southwest at 10 mi/ hr. (at) Give the vector representing the actual movement of the boat. [12 points] 72 , A \3 .1 V903" C ’; Cu (TV-4A} a '— (lkL-szaA WWW; ‘° ' > \o= 23:“ , €=~><€~x§ "b 1: .. ~ 9 2, _ if? \M \\e\\ \0 c. 2x ::> x- E M “”C+\°"\h23ﬁ L5-.9,23\ (b) What is the speed of the boat, relativemWW‘“ “a“: 5??? 25+ ﬁg 4 . MATH 223 SECTION 12 - FALL 2009 — EXAM 1 5. (a) Let f(:c, y, z) = \$2 + 22 — y. Sketch the level surface f = 1. Justify your work by describing and/or plotting cross sections. [12 points] Q“ S‘ X“; W S ‘1 xagm I \l QIX X”: C, I ?m\ao\¢x (\N.‘ L'( MA 2 M £1" SEX 1?: C, l ?£\rn\rrap\u§ Wk; \‘t MA K LL‘ £15K 5": C, C; {EAL Nb K “NA 2 Kim/xx“ {Q C 5 ’ h (b) 3Represent the level surface g(\$,y,z) = 42: — 2m + By = 4 as a function of two variables .7: and y. [8 points] MATH 223 SECTION 12 - FALL 2009 - EXAM 1 5 6. Match the contour diagrams with the surfaces. Give brief reasons for your choices. [10 points] ...
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