New York City is located at 40N latitude, 74W longitude. Moscow is located at 55N latitude,...

 

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New York City is located at 40N latitude, 74W longitude. Moscow is located at 55N latitude, 37E longitude. Think of the earth as a perfect sphere of radius 3960 miles centered at the origin with the North Pole on the positive part of the z-axis and the positive part of the x-axis passing through the prime meridian. Use the dot product (and a calculator) to answer the following: a. Compute the coordinates of both of these cities in xyz-space. b. What is the angle between the position vectors for these two cities? c. The shortest distance along the surface of a sphere from one point to another is the length of an arc on the great circle defined by those two points. Recalling that the length, s, of an arc of angle a on a circle of radius r is given by s ra, compute the shortest distance along the surface of the earth between New York and Moscow. New York City is located at 40N latitude, 74W longitude. Moscow is located at 55N latitude, 37E longitude. Think of the earth as a perfect sphere of radius 3960 miles centered at the origin with the North Pole on the positive part of the z-axis and the positive part of the x-axis passing through the prime meridian. Use the dot product (and a calculator) to answer the following: a. Compute the coordinates of both of these cities in xyz-space. b. What is the angle between the position vectors for these two cities? c. The shortest distance along the surface of a sphere from one point to another is the length of an arc on the great circle defined by those two points. Recalling that the length, s, of an arc of angle a on a circle of radius r is given by s ra, compute the shortest distance along the surface of the earth between New York and Moscow.