Finding Position Vectors and Particle Locations in 3-Dimensional Motion

[ducdat231]

Can someone please help me with this?

Homework Statement

A particle begin to travel (in 3-d dimension) at time t=pi with the direction vector d=-sin(t)i+cos(t)j+k

2. The attempt at a solution
Find the position vector r of that particle and the location of that particle at time t=2pi

I depressingly need some helps with this problem. You can just simply give me some idea or method and don't have to solve it step by step. Thanks a bunch!

 

[HallsofIvy]

$$\frac{dx}{dt}= -sin(t)$$
$$\frac{dy}{dt}= cos(t)$$
[tex]\frac{dz}{dt}= 1[/itex]
You can solve for x, y, and z by integrating. You will, however, need to know some "initial condition" to solve for the three "constants of integration" you will get. The problem says the particle starts moving at time t= pi. Doesn't the problem give a position for the particle at that time?

 

[ducdat231]

I'm sorry, my bad, the particle was traveling in the helical path r=cos(t)i+sin(t)+tk but at t=pi it changed and took the tangential path to the initial path. So I figured out it would travel on the direction of the velocity vector which I was given as the direction vector.