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Analytical Mech Homework Solutions 1

Analytical Mech Homework Solutions 1 - CHAPTER 1...

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CHAPTER 1 FUNDAMENTAL CONCEPTS: VECTORS 1.1 (a) A B ˆ ˆ ˆ ˆ ˆ ˆ ˆ ( ) ( ) 2 i j j k i j k + = + + + = + + K K 1 2 (1 4 1) 6 A B + = + + = K K (b) 3 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ 3( ) 2( ) 3 2 A B i j j k i j = + + = + K K k (c) (1)(0) (1)(1) (0)(1) 1 A B = + + = K K (d) ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1 1 0 (1 0) (0 1) (1 0) 0 1 1 i j k A B i j k i j k × = = + + = + K K 1 2 (1 1 1) 3 A B × = + + = K K K K 1.2 (a) ( ) ( ) ( ) ˆ ˆ ˆ ˆ ˆ 2 4 (2)(1) (1)(4) (0)(1) 6 A B C i j i j k + = + + + = + + = K ( ) ( ) ˆ ˆ ˆ ˆ 3 4 (3)(0) (1)(4) (1)(0) 4 A B C i j k j + = + + = + + = K K K (b) ( ) 2 1 0 1 0 1 8 0 4 0 A B C × = = − K K K ( ) ( ) 8 A B C A B C × = × = − K K K K K K (c) ( ) ( ) ( ) ( ) ( ) ˆ ˆ ˆ ˆ ˆ ˆ 4 2 4 4 8 A B C A C B A B C i k j i j k × × = = + =
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