test1_sol_Winter_08

# test1_sol_Winter_08 - l\t1ATH 2008/09E N AME(PLEASE PRINT):...

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Unformatted text preview: l\t1ATH 2008/09E N AME(PLEASE PRINT): Test . 1 January 29, 2008 . STUDENT NO .: ~ Instructions: 1. This test has 4 questions and a total of 40 marks. 2. Calculators are NOT allowed. sMt. . z (Ql) L1 L2 Given the parallel lines : ;T = 1 + 2t, y = 2 + 4t, z = 3 - 4t and : :17 = -1 - t, y = 1 - 2/, = -2 + 2t; L2. (a) [8 I\Iarks] Find the distance between L1 and -) ~ ?l :.::: - I l- \.> \ ) r.z c::. r 2") .~ ( \) l-/ ?> ) = (-'2) --I) -5) -') -") 'P, fl--)<.Vz. d \ '3(- ut) 3-, \') \ -=------::. -;3'\!~-+-q -t-I ~ --~- \ (_\)_~)2)\ J+Lf-t-4 (b) [9 Marks] Find a scalar equation of the plane containing the lines L1 and L2. ij7l-'3j ~~ -rD.==.d 5k-!'PZ (_\.>\/_2.) +0 ~.;JU IS J.d tvY1 ow-..a 12--jca./f( ~ Cern rs-/6 HUL ftu7 L, ~ L 2 . (Q2) [8 ~Iarks] For what value(s) of C do the lines Lj 'r; = (-1 + (?,c2, 1) + t(l, -1, -1) and L2: r~ = (0, c2, 1) + s(l, 1,-1 ) intersect? Find the point of intersection if there is any. : LJ ~ L2- . _\ . -r CZ . 1 _ -rc - -L~ =~~-~ ~ = . c::-\ IL Ct==o =1 eN 1t=u (Q3) [4 :MarksJ Sketch the graph of the cylinder z = 1 + :r2 1..- , -t ';l ~';t;::,l A " "~ " / (Q4) Consider the surface 4:r2 + 9Z2 = -36y; (a) [6 l'vIarks]Find and identify all traces of the surface (in particular, .TY, yz and xz-traces) ; q ?L .L-::zZ. . -r z. q =- f 1--} (b)[5 ~Iarks] By using part (a) identify and sketch the surface. ,, \ - +-- -, ( \ -1\ I - ...
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## This note was uploaded on 05/26/2010 for the course MATH Math2008 taught by Professor Monadi during the Fall '08 term at Carleton.

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test1_sol_Winter_08 - l\t1ATH 2008/09E N AME(PLEASE PRINT):...

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