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Mathematic Methods HW Solutions 11

# Mathematic Methods HW Solutions 11 - -2 t 5.12 x-5 5 = y...

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Chapter 3 11 2.15 R = 2 2.16 R = 3 2.17 R = 2 2.18 R = 3 3.1 - 11 3.2 - 721 3.3 1 3.4 2140 3.5 - 544 3.6 4 3.11 0 3.12 16 3.16 A = - ( K + ik ) / ( K - ik ), | A | = 1 3.17 x = γ ( x p + vt p ), t = γ ( t p + vx p /c 2 ) 3.18 D = 3 b ( a + b )( a 2 + ab + b 2 ), z = 1 (Also x = a + 2 b , y = a - b ; these were not required.) 4.11 - 3 i + 8 j - 6 k , i - 10 j + 3 k , 2 i + 2 j + 3 k . 4.12 arc cos( - 1 / 2) = 3 π/ 4 4.13 - 5 / 3, - 1, cos θ = - 1 / 3 4.14 (a) arc cos(1 / 3) = 70 . 5 (b) arc cos(1 / 3) = 54 . 7 (c) arc cos r 2 / 3 = 35 . 3 4.15 (a) (2 i - j + 2 k ) / 3 (b) 8 i - 4 j + 8 k (c) Any combination of i + 2 j and i - k . (d) Answer to (c) divided by its magnitude. 4.17 Legs = any two vectors with dot product = 0; hypotenuse = their sum (or diFerence). 4.18 2 i - 8 j - 3 k 4.19 i + j + k 4.20 2 i - 2 j + k 4.22 Law of cosines 4.24 A 2 B 2 In the following answers, note that the point and vector used may be any point on the line and any vector along the line. 5.1 r = (2 , - 3) + (4 , 3) t 5.2 3 / 2 5.3 r = (3 , 0) + (1 , 1) t 5.4 r = (1 , 0) + (2 , 1) t 5.5 r = j t 5.6 x - 1 1 = y +1 - 2 = z +5 2 ; r = (1 , - 1 , - 5) + (1 , - 2 , 2) t 5.7 x - 2 3 = y - 3 - 2 = z - 4 - 6 ; r = (2 , 3 , 4) + (3 , - 2 , - 6) t 5.8 x 3 = z - 4 - 5 , y = - 2; r = (0 , - 2 , 4) + (3 , 0 , - 5) t 5.9 x = - 1, z = 7; r = - i + 7 k + j t 5.10 x - 3 2 = y - 4 - 3 = z +1 6 ; r = (3 , 4 , - 1) + (2 , - 3 , 6) t 5.11 x - 4 1 = z - 3 - 2 , y = - 1; r = (4 , - 1 , 3) + (1
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Unformatted text preview: , ,-2) t 5.12 x-5 5 = y +4-2 = z-2 1 ; r = (5 ,-4 , 2) + (5 ,-2 , 1) t 5.13 x = 3, y-3 = z +5 1 ; r = 3 i-5 k + (-3 j + k ) t 5.14 36 x-3 y-22 z = 23 5.15 5 x + 6 y + 3 z = 0 5.16 5 x-2 y + z = 35 5.17 3 y-z = 5 5.18 x + 6 y + 7 z + 5 = 0 5.19 x + y + 3 z + 12 = 0 5.20 x-4 y-z + 5 = 0 5.21 cos θ = 25 / ( 7 √ 30 ) = 0 . 652, θ = 49 . 3 ◦ 5.22 cos θ = 2 / √ 6, θ = 35 . 3 ◦ 5.23 cos θ = 4 / 21, θ = 79 ◦ 5.24 r = 2 i + j + ( j + 2 k ) t , d = 2 r 6 / 5 5.25 r = (1 ,-2 , 0) + (4 , 9 ,-1) t , d = ( 3 √ 3 ) / 7 5.26 r = (8 , 1 , 7) + (14 , 2 , 15) t , d = r 2 / 17 5.27 y + 2 z + 1 = 0 5.28 4 x + 9 y-z + 27 = 0 5.29 2 / √ 6 5.30 1 5.31 5 / 7 5.32 10 / √ 27...
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