(n-1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector `veca` with respect to the center of the polygon. Find the position vector of centre of mass.

Six point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.

Three particles each of mass m are placed at the corners of a right angled triangle as shown in figure if OA=a and OB=b, the position vector of the centre of mass is: .

If vec a and vec b are the position vectors of A and B respectively, find the position vector of a Point C in BA produced such that BC = 1.5 BA.

What is the position vector of centre of mass of two particles of equal masses?

Point masses m_1 and m_2 are placed at the opposite ends of a rigid rod of length L, and nelgligible mass. The rod is to be set rotating about an axis perpendicular to it. Find the position on this rod through which the axis should pass in order that the work required to set the rod rotating with angular velocity omega_0 should be minimum.

If z and bar z represent adjacent vertices of a regular polygon of n sides where centre is origin and if (Im(z))/(Re(z)) = sqrt(2) - 1 , then n is equal to:

Four charges of +4,-3,+2 and +3 coulomb are placed at the corners of a square of each side 1m. Find the electric field at the centre of the square. Given = epsilon_0 = 8.85 xx 10^-12 C^2N^-1m^-2

Three charges of +0.1 C each are placed at the vertices of an equilateral triangle of each side 1m. If the energy is supplied at the rate of 1.0 kw, how many hours would be required to move one of the charges on to the mid point of the line joining the other two? Given =1/(4piepsilon_0) = 9xx 10^9 N ^2C^-2

A pyramid with vertex at point P has a regular hexagonal base ABCDEF. Position vectors of points A and B are hati and hati+ 2hatj , respectively. The centre of the base has the position vector hati+hatj+sqrt3hatk . Altitude drawn from P on the base meets the diagonal AD at point G. Find all possible vectors of G. It is given that the volume of the pyramid is 6sqrt3 cubic units and AP is 5 units.

Let vec a and vec b be the position vectors of the points (3,-5) and (m,4) respectively. Find m if the vectors vec a and vec b are collinear.