If `A xx B={(,(p,q),(p,r)),(,(m,q),(m,r)):}}`, find A and B.

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

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi

If pnea,qneb,rnec and |{:(p,b,c),(a,q,c),(a,b,r):}|=0 then prove that p/(p-a)+q/(q-b)+r/(r-c)=2

Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, q-r),(r-p,r-q,0)|:}=0

If A = {p,q,r, s} and B = {1, 2, 3} , find which of the following is not a function from A to B?

Given that q^2-p r 0, then the value of {:|(p, q, px+qy), (q, r, qx+ry), (px+qy, qx+ry, 0) |:} is- a. zero b. positive c. negative \ d. q^2+p r

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

Let Delta=|{:(a,p,x),(b,q,y),(c,r,z):}|=16" then "Delta_1=|{:(p+x,a+x,a+p),(q+y,b+y,b+q),(r+z,c+z,c+r):}|=32

Let vec(p),vec(q),vec(r) be three unit vectors such that vec(p)xxvec(q)=vec(r) . If vec(a) is any vector such that [vec(a),vec(q),vec(r )]=1,[vec(a),vec(r),vec(p )]=2 , and [vec(a),vec(p),vec(q )]=3 , then vec(a)=