`mu _(0 ) mu _(r ) , mu =(B )/(H ) , I = (M )/(V ) = (m ) /(A ) , B = mu _(0) ( H +I ) l chi =(I)/(H) , chi +1 = mu _(r) `

Using the relation vec(B) = mu_(0) (vec(H)+ vec(M)) , show that X_(m) = mu_(r) - 1 .

If a = I + j + k, b = i+ j, c = I and (a xx b) xx c = lambda a + mu b , then lambda + mu =

Find the shortest distance between the following (1-4) lines whose vector equations are : (i) vec(r) = (lambda - 1) hati + (lambda -1) hatj - (1 + lambda ) hatk and vec(r) = (1 - mu) hat(i) + (2 mu - 1) hatj + (mu + 2) hatk (ii) vec(r) = (1 + lambda) hati + (2 - lambda) hatj + (1 + lambda) hatk and vec(r) = 2 (1 + mu) hati - (1 - mu) hatj + (-1 + 2mu ) hatk .

In the given loop the magnetic field at the centre O is 1) (mu_0I)/(4) ( (r_1 + r_2)/(r_1 r_2) ) out of the page 2) (mu_0I)/(4) ( (r_1 + r_2)/(r_1 r_2)) into the page 3) (mu_0I)/(4) ( (r_1 - r_2)/(r_1 r_2)) out of the page 4) (mu_0 I)/(4) ( (r_1 - r_2)/(r_1r_2) ) into the page

Find the accelerations of blocks A and B for the following cases. (A) mu_(1)=0 " and "mu_(2)=0.1" (P)" a_(A)=a_(B)=9.5m//s^(2) (B) mu_(2)=0 " and "mu_(1)=0.1 " (Q)"a_(A)=9m//s^(2), a_(B)=10m//s^(2) (C) mu_(1)=0.1 " and "mu_(2)=1.0 " (R)"a_(A)=a_(B)=g=10m//s^(2) (D) mu_(1)=1.0 " and "mu_(2)=0.1 " (S)" a_(A)=1, a_(B)=9m//s^(2)