Question

1. a centripetal-acceleration addict rides in uniform circular motion with period T=2s and radius r=3m. at t1 his acceleration vector= 6(m/s^2)i + -4(m/s^2)j. At that instant, what are the values of vector b (dot) vector a

and vector r (dot) vector a

All I could figure out was that through this formula: T=(2(pi))r/T
V=9.425m/s

how do you make that into a vector though? and how do you find the r vector? is there a way to find the angle theta?

Answer 1

Vectors r, a and b have not been defined in the question. Perhaps these are notations used in your class and are obvious to you.
Please define what they are (velocity, acceleration, radial, tangential...)
I suppose unit vectors i, j are parallel to the x,y-axes respectively.

Answer 2

You have correctly calculated the tangential speed of
V=9.425m/s (=2pi*r/T)

Answer 3

The answer is zero because the angle between the two vectors is 90. Cos(90)= 0