Question: Points A = (6,0,0), B = (0, 6,0), and C = (4,4,2) are three points on the surface of the sphere given by x 2

Points A = (6,0,0), B = (0, 6,0), and C = (4,4,2) are three points on the surface

of the sphere given by x2+y2+z2 = 36.

(a) A bug begins to crawl on the surface of the sphere, starting at the point A towards the point

B. After passing through an are of 60, it stops at point P. What are the coordinates of the

bug at P?

(b) Find the shortest distance the bug would travel on the surface of the sphere if it were to go

from A to C.

bug could go directly through the sphere. Use vectors to get your result.

(d) There is a circle of radius 6 that passes through points A and B. What is the shortest distance from point C to this circle traveling along the surface of the sphere?

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