Question

A particle is located at the vector position = (2.00î + 4.00ĵ) m and a force exerted on it is given by = (4.00î + 3.00ĵ) N. a) What is the torque acting on the particle about the origin? r = _____________ N * m

Answer 1

given position vector with respect to origin r = 2.00 i + 4.00 j in meter

force f = 4.00 i + 3.00 j in newton

where i and j are the unit vectors along x and y axis  

torque = r x f = (2.00 i + 4.00 j ) $\times$   (4.00 i + 3.00 j)

= 2.00 i x 4.00 i + 2.00 i x 3.00 j + 4.00 j x 4.00 i + 4.00 j x 3.00 j

= 0 + 6.00 k -16.0 k + 0

= -10.0 k Nm

where k - unit vector along z - axis

[pls note ixi = jxj = kxk= 0, ixj = k, jxk = i, kxi = j and jxi= -k, kxj = -i, ixk = -j]