Ch03-p055 - 55 The two vectors are given by i j i j A = 8.00(cos130 sin130 = 5.14 6.13 i j i j B = B B = 7.72 9.20 x y(a The dot product of 5 A B

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55. The two vectors are given by ˆˆ ˆ ˆ 8.00(cos130 i sin130 j) 5.14i 6.13 j ˆ ˆ i j 7.72i 9.20 j. xy A BB B + ° = + =+= G G (a) The dot product of 5 AB G G is 5 5( 5.14i 6.13 j) ( 7.72i 9.20 j) 5[( 5.14)( 7.72) (6.13)( 9.20)] 83.4. ⋅=− + ⋅− = − + =− G G (b) In unit vector notation 3 ˆ ˆ 4 3 12 12( 5.14i 6.13 j) ( 7.72i 9.20 j) 12(94.6k) 1.14 10 k AB AB ×= × + × = = × GG (c) We note that the azimuthal angle is undefined for a vector along the z axis. Thus, our result is “1.14 × 10 3 , θ not defined, and φ = 0 ° .” (d) Since A is in the xy plane, and A B × G G is perpendicular to that plane, then the answer is
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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