ps01_soln - Physics 116, Fall 2007 Problem Set 1 due Sep 5,...

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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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ps01_soln - Physics 116, Fall 2007 Problem Set 1 due Sep 5,...

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