2 Here we'll consider two points A and B at the surface of the Earth (see Figure). We'll assume the Earth is spherical with radius R. a) Write down the straight-line distance d between A and B in terms of R and the angle a. Hint: use the law of cosincs. [2] (:1) Now we'll give point A the Cartesian coordinates (931,311,251) and point B the coordinates (:52, yg, 22). Write down an expression for d in terms of 9:1, x2,y1, yg, 21, 22. ' e) Now let point A have latitude and longitude 6'1 and (131, and point B latitude and longitude 6'2 and $2. Write down expressions for x1, y1 and zl in terms of 61 and (:51. Hint: don't forget to include R!' f) Using your answers to a), d) and e), nd an expression for oz in terms of 01, 02, 451 and $2. Hint: this will require use of trigonometric identities, and you'll get a simpler answer if you remember that cos(q51 7 $2) = cos qbl cos $2 + sin $1 sin $2. - " g) Using your answer to f), nd an expression relating a, 61 and 02 when the two longitudes are equal (451 = $2). Explain Why this answer makes sense