Let `vecr_1, vecr_2,……vecr_n` be the position of points `P_1,P_2,………,P_n` respectively relative to an origin O. Show that if the vector equation `a_1vecr_1+a_2vecr_2+..+a_nvecr_n=vec0` holds, then a similar equation will also hold good wilth respect to any other origin if `a_1+a_2+......+a_n=0`

Let vec r_1, vec r_2, vec r_3, , vec r_n be the position vectors of points P_1,P_2, P_3 ,P_n relative to the origin Odot If the vector equation a_1 vec r_1+a_2 vec r_2++a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a_1+a_2+dot+a_n=n b. a_1+a_2+dot+a_n=1 c. a_1+a_2+dot+a_n=0 d. a_1=a_2=a_3dot+a_n=0

Let r_(1),r_(2),r_(3), . . .,r_(n) be the position vectors of points P_(1),P_(2),P_(3), . . .,P_(n) relative to an origin O. show that if then a similar equation will also hold good with respect to any other origin O'. If a_(1)+a_(2)+a_(3)+ . . .+a_(n)=0 .

Lines vecr = veca _(1)+veca _(2)and vecr = veca _(2)+ vecb _(2) lie in a plane if :

The positions of two point charges q_(1) and q_(2) are vecr_(1) and vecr_(2) , respectively. Find the position of the point where the net field is zero due to thses charges.

Lines vecr = veca_(1) + lambda vecb_(1) and vecr = veca_(2) + svecb_(2) will lie in a Plane if

The equation of the plane which contains the origin and the line of intersectio of the plane vecr.veca=d_(1) and vecr.vecb=d_(2) is

The equation of the plane contaiing the lines vecr=veca_(1)+lamda vecb and vecr=veca_(2)+muvecb is

Write the vector form of force acting between two charges q_(1) and q_(2) having vecr_(1) and vecr_(2) as their position vectors respectively.

The vector equation of the pane passing through the intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(hati-2hatj)=-2 and the point (1,0,2) is