Analytical Mech Homework Solutions 1

Analytical Mech - CHAPTER 1 FUNDAMENTAL CONCEPTS VECTORS 1.1 j(a A B =(i k = i 2 k j j 1 2 A B =(1 4 1 = 6 j j(b 3 A 2 B = 3(i 2 k = 3i 2k j(c A B

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CHAPTER 1 FUNDAMENTAL CONCEPTS: VECTORS 1.1 (a) AB ˆˆ ˆ ˆ ˆ () ( ) 2 i j jk i jk +=+++=+ + K K 1 2 (1 4 1) 6 +=++ = K K (b) 32 ˆ 3 ( ) 2 3 2 AB ij j k ij −=+−+=+ K K k (c) (1)(0) (1)(1) (0)(1) 1 ⋅= + + = K K (d) ˆ ˆ ˆ 110 ( 10 ) ( 01 ) 011 ijk i j k i j k ×= = −+ −+ − =−+ K K 1 2 1 3 ×=++ = K K KK 1.2 (a) ˆ ˆˆ ˆ ˆ 2 4 (2)(1) (1)(4) 6 ABC i j i ⋅+ = +⋅++= + + = K ˆ ˆ 3 4 (3)(0) 4 i jk j +⋅= ++⋅= + + = K (b) 210 101 8 040 ⋅× = = K () () 8 ABC ABC ×⋅= ⋅×= (c) ( ) ( ) ( ) ˆ ˆ 42 4 4 8 A CB A B C ik j ×× =⋅ −⋅ = +− =−+ K K K 4 ( ) ( )
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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