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Mathematic Methods HW Solutions 28

# Mathematic Methods HW Solutions 28 - Chapter 6 11.1 11.4...

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Chapter 6 28 11.1 - 3 πa 2 11.2 2 ab 2 11.3 0 11.4 - 12 11.5 36 11.6 45 π 11.7 0 11.8 0 11.9 32 π/ 3 11.10 - 6 π 11.11 24 11.12 18 π 11.13 0 11.14 - 8 π 11.15 - 2 π 2 In the answers for Problems 18 to 22, u is arbitrary. 11.18 A = ( xz - yz 2 - y 2 / 2) i + ( x 2 / 2 - x 2 z + yz 2 / 2 - yz ) j + u 11.19 A = ( y 2 z - xy 2 / 2) i + xz 2 j + x 2 y k + u 11.20 A = i sin zx + j cos zx + k e zy + u 11.21 A = i y + u 11.22 A = i ( xz - y 3 / 3) + j ( - yz + x 3 / 3) + k ( x + y ) z + u 12.1 sin θ cos θ C 12.2 1 2 | B × A | 12.5 (a) - 4 π (b) - 16 (c) - 8 12.6 5 i - 8 j - 6 k 12.7 (a) 9 i + 5 j - 3 k (b) 29 / 3 12.8 2 / 5 12.9 24 12.10 (a) 2 i + j (b) 11 / 5 (c) 2 x + y = 4 12.11 (a) grad φ = - 3 y i - 3 x j + 2 z k (b) - 3 (c) 2 x + y - 2 z + 2 = 0, r = (1 , 2 , 3) + (2 , 1 , - 2) t 12.12 (a) 3 i + 2 j + k (b) 3 (c) 3 x + 2 y + z = 4, r = (0 , 1 , 2) + (3 , 2 , 1) t (d) (3 i + 2 j + k ) / 14 12.13 (a) 6 i - j - 4 k (b) 53 - 1 / 2 (6 i - j - 4 k ) (c) same as (a) (d) 53 1 / 2 (e) 53 1 / 2 12.14 (a)
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