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# a1 - PHYS2004(1st Term 10/11 Assignment 1 Section...

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PHYS2004 (1 st Term 10/11) 1 Assignment 1 Section A (Compulsory – due on 22/09/2010 Wed (before 5:00 pm )) 1. (a) Given that ˆ ˆ ˆ a i j k and ˆ ˆ ˆ 3 2 4 b i j k , find (i) the projection vector of a in the direction of b , and (ii) the projection vector of b in the direction of a . [30 marks] (b) Find numbers n 1 , n 2 and n 3 such that the vector 1 2 3 ˆ ˆ ˆ n n i n j n k is orthogonal to both ˆ ˆ ˆ a i j k and ˆ ˆ ˆ 3 2 2 b i j k . [30 marks] 2. Find a if the following vectors are coplanar: ˆ ˆ ˆ 2 A i j k , ˆ ˆ ˆ 3 2 B i j k , ˆ ˆ ˆ 2 C i j ak [40 marks] Section B (Optional Questions for STOT groups – please submit in STOT group sessions) 3. A 4-dimensional real vector , , , x y z t may be identified with the ordered pair , r t , where r is the 3-dimensional vector , , x y z . Such 4-dimensional

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a1 - PHYS2004(1st Term 10/11 Assignment 1 Section...

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