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**1. Homework Statement**

Show that the unit sphere {(x, y, z) : x^2 + y^2 + z^2 = 1} in R^3 is arcwise connected.

**2. Homework Equations**

**3. The Attempt at a Solution**

find a continous map f(t ) such that f( 0) = a, f(1 ) = b. a, b, in R^3 and are on the unit sphere. then show for every t in [0,1] f(t ) is on the sphere. just having trouble finding the right f . Tried f = ta + (1-t)b but only noticed that it is a line segment , so it should be wrong..