Test 3-math 1025 class test 3

Test 3-math 1025 class test 3 - York University Faculty of...

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Unformatted text preview: York University Faculty of Arts, Faculty of Science Math 1025 Class Test 3 NAME (print): (Family) . I (Given) l a SIGNATURE: J STUDENT NUMBER: _ _ l/ Instructions: | 1. Time allowed: 50 minutes P3 There are 5 questions on ?? pages. Answer all questions. e90 . Your work must justify the answer you give. 5. No calculators or other aids permitted. Page 1 MATH 1025 Test 3 March 17, 2006 1. Consider the lines l1 :(m,y,'z)=(1,0,5) +t (—1,1,2) and Z2 :(m,y,z)=(1,0, —1) +t (2, —2,2). ~ (5 points) Show that l1 and Z2 intersect, and find their point of intersection. . i.) {'5 ”“""§‘ Xf‘ifz‘: W...“ :— __—m éfigéa5fi5 3.. [+26 .,-- "(r w...— I g .1 ZC‘ gig—35:"! \ ~ : _‘ ,zC -:~ . @ (my 1+ WM! Es. (mfé-KS’eafif—‘mm ' Fa trut— if 2"? 4/5 (b) (2 points) Show that l1 and Z2 are perpendicular. b / Cineoé (vi/[yam v22) ~O. _ / / N (we, )(2) ~r— 0) 0—2) '+ 62> (2) ' O p f / / - / I _ C r /Q 0—1, MIA/O Hf I Check Page 2 MATH 1025 Test 3 March 17, 2006 2. (6 points) Let 7: (2, ~1, 1) and 7: (1, —1,3). Write 7: 171 + 172 where E is parallel to V and E is orthogonal to 7. A “.4— b H M w) A MATH 1025 Test 3 3. Let P = (3, —1, 1), Q = (4,1,0), R = (2, —g3,0). (a) (5 points) Calculate the area of APQR. (f; 75? —= (1-2;!) I 753': (02/ pl), j; Fix-Fe =/;Zd,’,< /:«%+2J Fifi“! lli‘ixfelfs W“? Z “20 firea. :5 3 U \ Z chm/Cl, wee/M» H X H 73 Page 3 March 17, 2006 a (3? (b) (3 points) Determine the distance from the point P to the line thr/ong \ Q and R. A r“; / 62a Sci—2,4,0) fit ’ // é-ENZMfiLfiL/é: EC) 42—74255 :— - Page 4 MATH 1025 Test 3 March 17, 2006 4. (6 points) Find all values of (1 such that the distance between the plane 211: — y —- 22 + d = 0 and the Plane2x—y—2z+3=0isoneunit. (flawl/ 4 0.00m few W m w m < («Ccfk an/fi MATH 1025 5. Page 5 Test 3 March 17, 2006 (a) (4 points) Prove that the function T given by T (x, y)=(a: + 1331,22: — y) is not a linear function. Note: It is not sufficient to observe that the formula is not given in the correct form. "’7"? 6 9 / i / "z 2 / ,_> 7(5) 7; [- fig 7A ,2. TC; x) q weK CM (7 h: 75X“ m fwd C 9 b J / i 11 / / , ' \Al/‘I/CM C' (fl—f/(UL 3( ' v / A f \ ~I _ ./ > (b) (4 points) Reflection in the line y = 3a: is a linear function T : R2 —> R2. Given that ——v T (1,0)=(—%, and T (0,1)=(%, g) write the standard matrix for T and use it to determine —> the reflection of the vector (—5, 10) in the line y = 3:17. The end ...
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Test 3-math 1025 class test 3 - York University Faculty of...

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