Hey prasum.
Show us what you have tried (but as a hint: you should get quadratic functions in your final displacement vectors when seen as a function of time).
at time t=0 particle is located at (1,2,3) it travels in a straight line to the point (4,1,4) has a speed 2 at (1,2,3) and a constant acceleration 3i-j+k find the equation for the position vector r(t) of the particle at time t.
do i have to apply equation of motion in this
i used vx=ux+axt (vx=velocity of particle along x axis)
and similarly vy and vz but i donts know the components of u ie ux,uy,uz all we know is that u=2m/s
then i used s=ut+1/2at2 along x,y and z axis respectively but if i do know ux how will i solve the equation
Use your initial conditions: You have r(t) (r is a vector with r<x(t),y(t),z(t)>) and r(0) so solve for your initial conditions.
The only thing you will have to decide is the starting velocity and the object is still before it moves then v(0) = 0 (or the zero vector).
You also need to add a constant of integration for the displacement and use your initial condition to get the constant (which will equal the starting position of the object).