Mathematic Methods HW Solutions 26

Mathematic Methods HW Solutions 26 - 4.10 V × d V/dt...

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Chapter 6 3.1 ( A · B ) C = 6 C = 6( j + k ), A ( B · C ) = - 2 A = - 2(2 , - 1 , - 1), ( A × B ) · C = A · ( B × C ) = - 8, ( A × B ) × C = 4( j - k ), A × ( B × C ) = - 4( i + 2 k ) 3.2 B · C = - 16 3.3 ( A + B ) · C = - 5 3.4 B × A = - i + 7 j + 3 k , | B × A | = 59, ( B × A ) · C / | C | = - 8 / 26 3.5 ω = 2 A / 6, v = ω × C = ( 2 / 6 ) ( - 3 i + 5 j + k ) 3.6 v = ( 2 / 6 ) ( A × B ) = ( 2 / 6 ) ( i - 7 j - 3 k ), r × F = ( A - C ) × B = 3 i + 3 j - k , n · r × F = [( A - C ) × B ] · C / | C | = 8 / 26 3.7 (a) 11 i + 3 j - 13 k (b) 3 (c) 17 3.8 4 i - 8 j + 4 k , 4, - 8, 4 3.9 - 9 i - 23 j + k , 1 / 21 3.12 A 2 B 2 3.15 u 1 · u = - u 3 · u , n 1 u 1 × u = n 2 u 2 × u 3.16 L = m [ r 2 ω - ( ω · r ) r ] For r ω , v = | ω × r | = ωr , L = m | r 2 ω | = mvr 3.17 a = ( ω · r ) ω - ω 2 r ; for r ω , a = - ω 2 r , | a | = v 2 /r . 3.19 (a) 16 i - 2 j - 5 k (b) 8 / 6 3.20 (a) 13 / 5 (b) 12 4.2 (a) t = 2 (b) v = 4 i - 2 j + 6 k , | v | = 2 14 (c) ( x - 4) / 4 = ( y + 4) / ( - 2) = ( z - 8) / 6, 2 x - y + 3 z = 36 4.3 t = - 1, v = 3 i + 3 j - 5 k , ( x - 1) / 3 = ( y + 1) / 3 = ( z - 5) / ( - 5), 3 x + 3 y - 5 z + 25 = 0 4.5 | d r /dt | = 2; | d 2 r /dt 2 | = 1; path is a helix. 4.8 d r /dt = e r ( dr/dt ) + e θ ( rdθ/dt ), d 2 r /dt 2 = e r [ d 2 r/dt 2 - r ( dθ/dt ) 2 ] + e θ [ rd 2 θ/dt 2 + 2( dr/dt )( dθ/dt
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Unformatted text preview: )]. 4.10 V × d V /dt 6.1-16 i-12 j + 8 k 6.2-i 6.3 6.4 πe/ (3 √ 5) 6.5 ∇ φ = i-k ;-∇ φ ; dφ/ds = 2 / √ 13 6.6 6 x + 8 y-z = 25, ( x-3) / 6 = ( y-4) / 8 = ( z-25) / (-1) 6.7 5 x-3 y + 2 z + 3 = 0, r = i + 2 j-k + (5 i-3 j + 2 k ) t 6.8 (a) 7 / 3 (b) 5 x-z = 8; x-1 5 = z +3-1 , y = π/ 2 6.9 (a) 2 i-2 j-k (b) 5 / √ 6 (c) r = (1 , 1 , 1) + (2 ,-2 ,-1) t 6.10 j , 1,-4 / 5 26...
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This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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