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Math252FinalF06

# Math252FinalF06 - Math 252 Name FINAL MATH 252 FALL 2006...

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Math 252 Name: ________________________ FINAL MATH 252 – FALL 2006 – KUNIYUKI 60 POINTS TOTAL (15 PROBLEMS; 4 POINTS EACH) No books allowed. An appropriate sheet of notes and a scientific calculator are allowed. 1) What is the geometric definition of the dot product of two vectors a and b in V n ? Circle one: a) a b = a b cos θ b) a b = a b sin θ c) a b = a b tan θ 2) Give symmetric equations for the line in xyz -space that passes through the point 7, 4, 2 ( ) and that has direction vector 3 i 2 j + k . 3) The graph of 3 x 2 + 4 y 2 z = 0 in xyz -space is … (circle one): a) A Cone b) An Ellipsoid c) An Elliptic Paraboloid d) A Hyperbolic Paraboloid e) A Hyperboloid of One Sheet f) A Hyperboloid of Two Sheets

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4) A plane curve C is parameterized by r , a smooth vector-valued function of t , from t = a to t = b , where a < b . The curve does not overlap itself. Which of the following will give you the arc length of C ? Circle one: a) r t ( ) dt a b b) r t ( ) dt a b c) ′′ r t ( ) dt a b 5) True or False: If v
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