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a2 - PHYS2004(1st Term 10/11 Assignment 2 Section...

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PHYS2004 (1 st Term 10/11) 1 Assignment 2 Section A (Compulsory – due on 30/09/2010 Thu (before 5:00 pm)) 1. Show that the four points: 1,1, 0 A , 2, 0, 1 B , 2,1, 2 C and 4, 4, 1 D are coplanar and find the equation of the plane containing them. [50 marks] 2. Find the Cartesian equation of (a) an infinite right circular cone with vertex at origin 0, 0, 0 and angle with the axis along 1 ˆ ˆ ˆ ˆ 3 n i j k . [25 marks] (b) a right circular cylinder of radius a with axis along 1 ˆ ˆ ˆ ˆ 3 n i j k . [25 marks] Section B (Optional Questions for STOT groups – please submit in STOT group sessions) 3. Given that 1 a , 2 a and 3 a are vectors such that 1 2 3 1 a a a . (i) If 1 1 2 2 3 3 r a a a , express i in terms of r , 1 a , 2 a and 3 a . (ii) r may also be expressed in the form: 1 1 2 2 2 3 3 3 1 r a a a a a a
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