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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)
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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.)
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@ (my 1+ WM! Es. (mféKS’eaﬁf—‘mm ' Fa trut— if 2"? 4/5 (b) (2 points) Show that l1 and Z2 are perpendicular. b /
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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? —= (12;!) I 753': (02/ pl),
j; FixFe =/;Zd,’,< /:«%+2J
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lli‘ixfelfs W“? Z “20
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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“; /
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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
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\ ~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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This note was uploaded on 09/28/2010 for the course MATH 1025 taught by Professor Tammie during the Fall '10 term at York University.
 Fall '10
 Tammie
 Math, Linear Algebra, Algebra

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