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Unformatted text preview: Physics 116, Fall 2007 Problem Set 1 due Sep 5, 2007 Figures are included at the end of the solution set. 1. Vector operations Given two vectors A = 2 i + j 4 k and B = i +3 j +2 k , find: a) A + B , b) A B , c) A B , d) A B . SOLUTION: a) A + B = (2 i + j 4 k ) + ( i + 3 j + 2 k ) = (2 1) i + (1 + 3) j + ( 4 + 2) k = i + 4 j 2 k b) A B = (2 i + j 4 k ) ( i + 3 j + 2 k ) = (2 + 1) i + (1 3) j + ( 4 2) k = 3 i 2 j 6 k c) A B = (2 i + j 4 k ) ( i + 3 j + 2 k ) = (2)( 1) + (1)(3) + ( 4)(2) = 7 d) A B = i j k 2 1 4 1 3 2 = [(1)(2) ( 4)(3)] i [(2)(2) ( 4)( 1)] j + [(2)(3) (1)( 1)] k = 14 i + 7 k 2. Vector operations Kleppner and Kolenkow (K&K) 1.4. SOLUTION:  A B  2 =  A + B  2 A 2 + B 2 2 A B = A 2 + B 2 + 2 A B A B = 0 AB cos = 0 = 2 3. Coordinate systems K&K 1.10. SOLUTION: From graph, you could read off r 1 = xr r 1 r 2  r 1 r 2  + A = x ( r 1 r 2 ) + A A = r 1 x ( r 1 r 2 ) = (1 x ) r 1 + x r 2 1 4. Coordinate systems A plane can be uniquely specified by a vector...
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 Fall '05
 ELSER, V
 Physics

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