Deduce an expression for the electric field `vecE` due to a system of two harges `q_1 and q_2` with position vectors `vecr_1 and vecr_2` at a oint `vecr` w.r.t the common origin O.

Find out the expression for the potential energy of a system of three point charges q_1, q_2 and q_3 located at vecr_1, vecr_2 and vecr_n w.r.t the common origin O.

Deduce the expression for the potential energy of a system of two point charges q_1 and q_2 brought from infinity to the points vecr_1 and vecr_2 respectively in the presence of electric field vecE .

Write the vector form of force acting between two charges q_1 and q_2 having vec r_1 and vec r_2 as their position vectors respectively.

Supposing Newton's law of gravitational for gravitation fores vecF_1 and vecF_2 between two masses m_1 and m_2 at positions vecr_1 and vecr_2 read vecF_1 = - vecF_2 = - (vecr_12)/(r_12^3) GM_0^1((m_1m_2)/(m_0^2))^n where M_0 is a constant of dimension of mass. vecr_12 = vecr_1 - vecr_2 and n is a number. In such a case

Find the position vector of the point R which divides the line (segment) joining the two points P and Q with position vectors vec(OP) = 2 vec a+ vec b and vec (OQ) = vec a-2 vec b respectively, in the ratio 1: 2. (i) internally (ii) externally. ‘

Graphically, represent the variation of electric field due to a point charge Q with 1//r^2 where r is the distance of the obervation point from the charge.

A charge Q located at a point rarrr is in equilibrium under the combined electric field of three charges q_1, q_2 and q_3 if the charges q_1, q_2 are located at the points rarrr_1 and rarrr_2 respectively, find the direction of the force on Q, due to q_3 , in term of q_1,q_2,q_3 rarrr, rarrr_1, and rarrr_2

Find the position vector of the mid point of the vector joining the points P(2,3,4), Q(4,1,-2)