Force `vecF=(2.0N)hati-(3.0N)hatk` acts on a pebble with position vector `vecr=(0.50m)hatj-(2.0m)hatk` relative to the origin. In unit-vector notation, what is the resulting torque on the pebble about the origin ?

A big olive (m=0.50 kg) lies at the origin of an xy coor dinate system, and a big Brazil nut (M = 1.5 kg) lies at the point (1.0,2.0) m. At t=0, a force vecF_o = (2.0hati + 3.0hatj)N begins to act on the olive, and a force vecF_n = (-3.0hati – 2.0hatj)N begins to act on the nut. In unit-vector notation, what is the displacement of the center of mass of the olive-nut system at t = 4.0 s, with respect to its position at 1= 0?

A force vecF=(6.00hati-4.00hatj)N acts on a particle with position vector vecr=(-3.00hati+1.00hatj)m . Find (a) the torque about the origin acting on the particle and (b) the angle between vecrandvecF .

A force vecF=2hati +hatj-hatk acts at point A whose position vector is 2hati-hatj. Find the moment of force vecF about the origin.

In a particle accelerator, the position vector of a particle is initially estimated as vecr=6.0hati-7.0hatj+3.0hatk and after 10 s, it is estimated to be vecr=-3.0hati+9.0hatj-3.0hatk , all in meters. In unit vector notation, what is the average velocity of the particle?

A force F=(2hati+3hatj-hatk)N is acting on a body at a position r=(6hati-3hatj-2hatk) . Calculate the torque about the origin

A particle moves through an xyz coordinate system while a force acts on the particle. When the particle has the position vector vecr=(2.00m)hati-(3.00m)hatj+(2.00m)hatk , the force is given by vecF=F_(x)hati+(7.00N)hatj-(6.00N)hatk and the corresponding torque about the origin is vectau=(400N*m)hati+(2.00N*m)hatj-(1.00N*m)hatk . Determine F_(x) .

A force (hati-2hatj+3hatk) acts on a particle of positive vector (3hati+2hatj+hatk) . Calculat the torque acting on the particle.

A force (hati-2hatj+3hatk) acts on a particle of position vector (3hati+2hatj+hatk) . Calculate the hatj^(th) component of the torque acting on the particle.

A force vecF=(2hati+3hatj+4hatk)N displaces a body from position vector vec(r_(1))=(2hati+3hatj+hatk)m to the positive vector vec(r_(2))=(hati+hatj+hatk)m . Find the work done by this force.