test1_sol_Winter_08

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 - ...
View Full Document

This note was uploaded on 05/26/2010 for the course MATH Math2008 taught by Professor Monadi during the Fall '08 term at Carleton.

Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online