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# DOC060 - Name Student Q1_Q2_Q3_Q4=_Q5_Q6 Total UNIVERSITY...

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Unformatted text preview: Name: Student #: Q1 __Q2 __Q3 __Q4=__Q5 __Q6 __ Total UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING MAT190F — Vector and Matrix Algebra Term Test October 2, 2006 Instructor — W.R. Cluett Closed Book All work to be marked must appear on front of page. Use back of page for rough work only. Given information: -' -' X1 X2 ylzZ _Z1y2 .. -+ u-v _... -d .. COSQZW; y1 X y2 : _(x122_21x2) ;pr0]3u=“g“2d u V Z] 22 x1y2_y1x2 1. Let P be the point (2,3,—2) and Q the point (7,—4,1). (a) Find the midpoint of the line segment connecting P and Q. (b) Find the point on the line segment connecting P and Q that is 3A of the way from P to Q. ~ 2. Find the (x, y) components of u , v , u + v, and u — v for the vectors shown in the ﬁgure below. 3. Find the angle between a diagonal of a cube and one of its faces (see ﬁgure below). Let 1:1: , it: and u: be the three sides of the cube of equal length. The angle you are looking for is «9 . 4. Find all unit vectors parallel to the yz—plane that are perpendicular to the vector [3 -1 2]? . The volume of the tetrahedron shown in the ﬁgure below is: l/3(area of base)(height) Use this result to prove that the volume of a tetrahedron whose sides are the _. _. u . 1 .. .. _. vectors a, b and C 1s -—|a-(b><c)]. 6 6. Find an equation for the plane, each of whose points is equidistant from (-1,-4,-2) and (CL-2,2). ...
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DOC060 - Name Student Q1_Q2_Q3_Q4=_Q5_Q6 Total UNIVERSITY...

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