If a, b, c be the pth, qth and rth terms respectively of a HP, show that the points (bc, p), (ca, q) and (ab, r) are collinear.

If a,b,c are the pth,qth,rth terms, respectively,of an HP,show that the points (bc,p),(ca,q), and (ab,r) are collinear.

If a,b,c are the pth,qth,rth terms, respectively,of an HP, show that the points (bc,p),(ca,q), and (ab,r) are collinear.

If a,b,c be the pth, qth and rth term respectively of H.P. show that the vectors bc veci+pvecj+veck, ca veci+q vecj+veck and ab veci+r vecj+veck are coplanar.

If a, b, c are the pth, qth, rth terms respectively of an H.P. , then the lines bcx + py+1=0, cax + qy+1=0 and abx+ry+1=0 (A) are concurrent (B) form a triangle (C) are parallel (D) none of these

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

If a,b,c, be the pth, qth and rth terms respectivley of a G.P., then the equation a^q b^r c^p x^2 +pqrx+a^r b^-p c^q=0 has (A) both roots zero (B) at least one root zero (C) no root zero (D) both roots unilty

If a,b,c are positive and are the pth, qth and rth terms respectively of a G.P., the the value of |(loga, p, 1),(logb, q, 1),(logc, r, 1)|= (A) 1 (B) pqr(loga+logb+logc) (C) 0 (D) a^pb^qc^r

If a,b,c be the pth , qth and rth terms of an A.P., then p(b-c) + q(c-a) + r(a-b) equals to :

If a,b,and c are positive and are the pth, qth and rth terms respectively of a GP. Show without expanding that |{:(loga,p,1),(logb,q,1),(logc,r,1):}|=0