A ardius vector of point A relative to the origin varies with time t as `vec(r)= at hat(j)-bt^(2) hat(j)` where a and b are constants. Find the equation of point's trajectory.

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

A particle move in x-y plane such that its position vector varies with time as vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j . Find the equation of the trajectory of the particle.

A particle move in x-y plane such that its position vector varies with time as vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j . Find the equation of the trajectory of the particle.

The vector vec A varies with time as vec A=that i-sin pi that j+t^(2)hat k. Find the derivative of the vector at t=1

The position vector of a particle is given by vec(r ) = k cos omega hat(i) + k sin omega hat(j) = x hat(i) + yhat(j) , where k and omega are constants and t time. Find the angle between the position vector and the velocity vector. Also determine the trajectory of the particle.

If vec(r)=[ucos theta(hat(i))+u sin theta(hat(j))]t+(1)/(2)g(-hat(j))t^(2) then calculate equation of trajectory.

Position vector of a particle is expressed as function of time by equation vec(r)=2t^(2)+(3t-1) hat(j) +5hat(k) . Where r is in meters and t is in seconds. Find the velocity vector

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

The vector equation vec(r)=(hat(i)-2hat(j)-hat(k))+t(6hat(j)-hat(k)) represents a straight line passing through the points