Engineering Calculus Notes 24

Engineering Calculus Notes 24 - P ( x,y,z ) (rectangular...

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12 CHAPTER 1. COORDINATES AND VECTORS describes the sphere of radius R centered at the origin, while φ = α describes a cone with vertex at the origin, making an angle α ( resp . π α ) with its axis, which is the positive ( resp . negative) z -axis if 0 < φ < π/ 2 ( resp . π/ 2 < φ < π ). Exercises for § 1.1 Practice problems: 1. Find the distance between each pair of points (the given coordinates are rectangular): (a) (1 , 1) , (0 , 0) (b) (1 , 1) , ( 1 , 1) (c) ( 1 , 2) , (2 , 5) (d) (1 , 1 , 1) , (0 , 0 , 0) (e) (1 , 2 , 3) , (2 , 0 , 1) (f) (3 , 5 , 7) , (1 , 7 , 5) 2. What conditions on the components signify that
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Unformatted text preview: P ( x,y,z ) (rectangular coordinates) belongs to (a) the x-axis? (b) the y-axis? (c) the z-axis? (d) the xy-plane? (e) the xz-plane? (f) the yz-plane? 3. For each point with the given rectangular coordinates, nd (i) its cylindrical coordinates, and (ii) its spherical coordinates: (a) x = 0, y = 1 , , z = 1 (b) x = 1, y = 1, z = 1 (c) x = 1, y = 3, z = 2 (d) x = 1, y = 3, z = 2...
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