4. (a) Check, from first principles, that the great circle through the points (0,0, 1) and...

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4. (a) Check, from first principles, that the great circle through the points (0,0, 1) and (1, 1, 1) on the unit sphere centred at the origin of R is a geodesic. [Hint: First parameterize it using an appropriate combination of trigono- metric functions. Then calculate the second derivative.] 4. (a) Check, from first principles, that the great circle through the points (0,0, 1) and (1, 1, 1) on the unit sphere centred at the origin of R is a geodesic. [Hint: First parameterize it using an appropriate combination of trigono- metric functions. Then calculate the second derivative.]