A body is projected up such that its position vector varies with time as `vecr = 6t hati+(8t-5t^2) hatj` . Find the time of flight.

A body is projected up such that its position vector varies with time as vecr = 6t hati+(8t-5t^2) hatj . Find the initial velocity.

The position vector vecr of a particle with respect to the origin changes with time t as vecr =Athati-Bt^2hatj, where A and B are positive constants. Determine (i) the locus of the particle,

The position vector vecr of a particle with respect to the origin changes with time t as vecr =Athati-Bt^2hatj, where A and B are positive constants. Determine (ii) the nature of variation with time of the velocity and acceleration vectors, and also the moduli of them.

Find the distance of the point with position vector 2 hati+ hatj- hatk from the plane vecr .( hati- 2 hatj+ 4 hatk)=9 .

Position vector of a particle is related to time t as vecr=(t^2-1)hati+2thatj . The locus of the particle on the x-y plane is

A particle moves in a straight line such that its distance x from a fixed point on it at any time t is given by x=1/4 t^4-2t^3+4t^2-7 . Find the time its velocity is maximum and the time when its acceleration is minimum.