Calculus Problem And Solution

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urgent problem! (Calculus) To solve this problem?

■ ■ ■ ■ ■ Please give me a detailed solution ■ ■ ■ ■ ■ 1.If vector = (1,0,3), vectorB = (5,2,6), findθAB =? 2.Show that vector delivery of 4.0, -1) the vector b (= = (1,3,4), vector c = (-5,-3.-3) form the sides of a triangle. Is this a right triangle? Calculate the area of triangle 3. (A) Convert the points P (1,3,5), T (0, -4.3) and S (-3, -4, -10) from Cartesian to cylindrical and spherical. (B) Transform vector vector Q = ([√ (² + y ² x) / √ (x ² + y ² + z ²)], 0,-z / √ (x + y + z ² ² ²)) A cylindrical and spherical coordinates (C) assess vector Q at T in the three coordinate systems 1.If the vector A = (1,0,3), vector B = (5,2,6), findθAB =?

1. cos.theta = A * B / (| A | * | B |) = (1 * 5 0 * 2 3 * 6) / 5 √ 26 = 81 171 2. assuming the angle of the vectors of A and B is "m" for cos m = a * b / (| A | * | b |) = 0 because cos90 = 0 m = 90 … so it is a right triangle … | A | and | b | represent the union between the right sides of the triangle 17. | A | = √, | B | = √ 26 = S | a | * | b | / 2 = 10.5 3. P (1,3,5) in cylindrical coordinates ……. r = 1 +9 = √ √ 10 …. θ = tan ^ (-1) 3 = 71.6 z = 5 In terms of x, y and z = x = √ r.cosθ 10 * 71.6 = 226 y = r.sinθ = 0.95 * √ 10 = 3 and z = 5 that (226,3,5) Idem, T 's of no cylindrical coordinates S' s cylindrical coordinates is (0.6, -0.8, -10) ………… ……….( this is all I know .. )

Stewart’s Calculus Problem 12.3.15


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