Q. #2: i) Find V(), if = In |7| ii) Prove that if A and B are non-collinear, then xA + yB = 0 implies x = y = 0 iii) Show that V(+) = V + . iv) If A = ti- tj + (2t + 1)k and B = (2t - 3)i + j - tk, then find (AxB) dt v) Show that the resultant R of three concurrent non-coplanar forces acting at origin of a parallelepiped with the given forces for its edges is represented by the diagonal. vi) State and prove Varigonon's Theorem. vii) Find the angle of friction when two bodies have a rough contact at a point O. viii) Find the least force to drag a particle on a rough horizontal plane. ix) Show that the magnitude of the moment is the product of the perpendicular distance between the components of the couple and magnitude of either component. x) State the principle of virtual work for a rigid body or a set of rigid bodies.