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assignment1 - MATH1211/10-11(2)/A1/NKT THE UNIVERSITY OF...

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MATH1211/10-11(2)/A1/NKT THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Assignment 1 Due date: 2011 January 24 (Monday), 5:00pm. (The Exercise/problem numbers in the following refer to those in the textbook.) Note: do not just give a numerical or yes/no answer. In your solution you have to show the steps of how you obtain your answer. 1. ( § 1.4 no.24) Suppose that a , b , and c are noncoplanar vectors in R 3 , so that they determine a tetrahedron (with the tails of a , b , c touching together to form a vertex of the tetrahedron, and the heads of a , b , c forming the remaining three vertices). Give a formula for the surface area of the tetrahedron in terms of a , b , c . (Note: More than one formula is possible.) 2. ( § 1.4 no.27) Verify that, for vectors a , b , c R 3 , ( a × b ) × c = ( a · c ) b - ( b · c ) a . 3. ( § 1.5 no.26) (a) The lines l 1 ( t ) = t (1 , - 1 , 5) + (2 , 0 , - 4) and l 2 ( t ) = t (1 , - 1 , 5) + (1
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assignment1 - MATH1211/10-11(2)/A1/NKT THE UNIVERSITY OF...

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