A force F = i + 3 j - 2 k acts on a particle whose position vector is r = 2 i - j + 4 k . If the torque acting on the particle about the origin is = -10 i + 12 j + 8 k , the value of is:

Step-by-step solution

The torque is given by the cross product of the position vector and the force vector: = r F = vmatrix i & j & k 2 & -1 & 4 & 3 & -2 vmatrix Expanding the determinant: = i [(-1)(-2) - (4)(3)] - j [(2)(-2) - (4)( )] + k [(2)(3) - (-1)( )] = -10 i + (4 + 4 ) j + (6 + ) k We are given that = -10 i + 12 j + 8 k . Equating the j components: 4 + 4 = 12 4 = 8 = 2 Equating the k components also gives 6 + = 8 = 2 . Answer: 2