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ps01_soln

# 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 ˆ i + ˆ j- 4 ˆ k and B =- ˆ i +3 ˆ j +2 ˆ k , find: a) A + B , b) A- B , c) A · B , d) A × B . SOLUTION: a) A + B = (2 ˆ i + ˆ j- 4 ˆ k ) + (- ˆ i + 3 ˆ j + 2 ˆ k ) = (2- 1) ˆ i + (1 + 3) ˆ j + (- 4 + 2) ˆ k = ˆ i + 4 ˆ j- 2 ˆ k b) A- B = (2 ˆ i + ˆ j- 4 ˆ k )- (- ˆ i + 3 ˆ j + 2 ˆ k ) = (2 + 1) ˆ i + (1- 3) ˆ j + (- 4- 2) ˆ k = 3 ˆ i- 2 ˆ j- 6 ˆ k c) A · B = (2 ˆ i + ˆ j- 4 ˆ k ) · (- ˆ i + 3 ˆ j + 2 ˆ k ) = (2)(- 1) + (1)(3) + (- 4)(2) =- 7 d) A × B = ˆ i ˆ j ˆ k 2 1- 4- 1 3 2 = [(1)(2)- (- 4)(3)] ˆ i- [(2)(2)- (- 4)(- 1)] ˆ j + [(2)(3)- (1)(- 1)] ˆ k = 14 ˆ i + 7 ˆ 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 θ = 0 → θ = π 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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