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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 .. +
uv _... 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 (CL2,2). ...
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 Fall '08
 Cluett

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