`P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1),` then find the projection length of ` vec P Qon vec R Sdot`

P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(3,-2,-1), then find the projection length of vec PQ and vec R Sdot

P(0, 3, -2), Q(3, 7, -1) and R(1, -3, -1) are 3 given points. Find vec (PQ)

If P(0, 1, 2), Q(4, -2, 1) and R(0, 0, 0) are three points, then anglePRQ is

A charge Q located at a point vec r is in equilibrium under the combined field of three charges q_(1), q_(2) and q_(3) . If the charges q_(1) and q_(2) are located at point vec r_(1) and vec r_(2) respectively, find the direction of the force on Q due to q_(3) in terms of q_(1),(q_2), vec r_(1) vec r_(2) , and vec(r) .

Consider the cube in the first octant with sides OP,OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where O(0,0,0) is the origin. Let S(1/2,1/2,1/2) be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If vec(p)=vec(SP), vec(q)=vec(SQ), vec(r)=vec(SR) and vec(t)=vec(ST) then the value of |(vec(p)xxvec(q))xx(vec(r)xx(vect))| is

The resultant vector of vec(P) and vec(Q) is vec(R ) . On reversing the direction of vec(Q) the resultant vector becomes vec(S) . Show that R^(2)+S^(2)=2(P^(2)+Q^(2))

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are

If vec r. vec a=0, vec r. vec b=1 \ and \ [[ vec r ,vec a, vec b]]=1, vec adot vec b!=0,( vec adot vec b)^2-| vec a|^2| vec b|^2=-1, then find vec r in terms of vec a \ and \ vec b .

If V=2r^(2) then find (i) vec(E) (1, 0, -2) (ii) vec(E) (r=2)

If | (a+1,a+2, a+p), (a+2, a+3,a+q), (a+3,a+4,a+r)|=0,then p ,q ,r are in: