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

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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 ai jk  and ˆ ˆ ˆ 32 4 bi jk  , 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 12 3 ˆ ˆˆ nn in jn k  is orthogonal to both ˆ ˆ ˆ  and ˆ ˆ ˆ 32 2  . [30 marks] 2. Find a if the following vectors are coplanar: ˆ 2 A ij k , ˆ B , ˆ 2 Ci j a k [40 marks] Section B (Optional Questions for STOT groups – please submit in STOT group sessions) 3. A 4-dimensional real vector   ,,, xyzt may be identified with the ordered pair  , rt , where r is the 3-dimensional vector   ,, xyz . Such 4-dimensional vectors can be multiplied according to the following definition:      11 2 2 1 2 1 2 2 2 1 2 , rt rt r r tr trt t r r 
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This note was uploaded on 10/14/2010 for the course PHYS 2051 taught by Professor Drkwong during the Spring '10 term at CUHK.

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

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