Problem number 1.37 only. Thanks!u
Extracted text: 1.30. Find the unit vector directed from (2, -5, –2) toward (14, -5, 3). 12 5 a.+ Ans. 13 1.31. Find the vector directed from (10, 37/4, x/6) to (5, x/4, x), where the endpoints are given in spherical coordinates. Аns. -9.66а, — 3.54а, + 10.61я, 1.32. Find the distance between (2, x/6, 0) and (1, x, 2), where the points are given in cylindrical coordinates. Ans. 3.53 1.33. Find the distance between (1, x/4, 0) and (1, 3x/4, x), where the points are given in spherical coordinates. Ans. 2.0 1.34. Use spherical coordinates and integrate to find the area of the region 0sosa on the spherical shell of radius a. What is the result when a = 2x? Ans. 2aa', A - 4ла" 1.35. Use cylindrical coordinates to find the area of the curved surface of a right circular cylinder of radius a and height h. Ans. 2nah 12 VECTOR ANALYSIS (CHAP. 1 1.36. Use cylindrical coordinates and integrate to obtain the volume of the right circular cylinder of Problem 1.35. Ans. na'h 1.37. Use spherical coordinates to write the differential surface areas dS, and dS, and then integrate to obtain the areas of the surfaces marked 1 and 2 in Fig. 1-14. Ans. л/4, л/6 dS 60 Fig. 1-14 1.38. Use spherical voondinates to find the volumuc of a litumispicrival sliel of iunei radius 2.00 m and outcr radius 2.02 m. Ans, 0.1627 m 1.39. Using spherical coordinates to express the differential volume, integrate to obtain the volume defined by Isrs2m, 0s0