Find the components along the `xyz` axes of the angular momentum I of a particle, whose position vector is r with components `x_2 y_3 z` and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-componenTt.

Two particles, each of mass m and speed v_3 travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

The position of a particle moving in xy plane at time t is given by x = (3t^2 -6) and y=(t^2-2t). Which one is correct statement for its motion?

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by F=-hati+2hatj+3hatk N where hatihatjhatk are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?

For what value of p the system equations, px-y=2, 6x-2y=3 has only one solution?

A particle moves along a curve 6y = x^3+2 . Find the points on the curve at which the y condinate is changing 8 times as fast as the x cordinate.