Find the position vector r(t) given the velocity v(t)=(10t²)i + 10sin(2t)j + 25t⁴k and the initial position vector r(0)=-2i + 3j - k.
a) r(t) = -2i + 3j - k + ∫(10t²)i dt + ∫10sin(2t)j dt + ∫25t⁴k dt
b) r(t) = -2i + 3j - k + (10/3)t³i - 5cos(2t)j + (5/5)t⁵k
c) r(t) = -2i + 3j - k + (10/3)t³i + 5sin(2t)j + (5/5)t⁵k
d) r(t) = -2i + 3j - k + (10/3)t³i + 5cos(2t)j + (5/5)t⁵k