# Thread: Vector-valued functions and motion in space #2

1. ## Vector-valued functions and motion in space #2

r(t) is the position of a particle in space at time t. Find the angle between the velocity and and acceleration vectors at time t=0.

$r(t)=(3t+1)i+(\sqrt{3})tj+t^{2}k,$

I can find the velocity and acceleration vectors easily. I just don't know how to find the angle between the vectors. Any help?

Nevermind, I found it.

$\theta = cos^{-1}(\frac{u\cdot v}{|u||v|})$

2. Find $\arccos \left( {\dfrac{{v(0) \cdot a(0)}}
{{\left\| {v(0)} \right\|\left\| {a(0)} \right\|}}} \right)$