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If P≡(1/x p ,p);Q≡(1/x q ,q);R≡(1/x r ,r) where x k ≠0,k=p,q,r belong to N,denotes the k th term of a harmonic progression,then a.Area(ΔPQR)={(p 2 q 2 r 2 )/2}√((p-q) 2 +(q-r) 2 +(r-p) 2 ) b.ΔPQR is a right angled triangle c.the points P,Q and R are collinear d.none of these

If P≡(1/xp,p);Q≡(1/xq,q);R≡(1/xr,r) where xk≠0,k=p,q,r belong to N,denotes the kth term of a harmonic progression,then


a.Area(ΔPQR)={(p2q2r2)/2}√((p-q)2+(q-r)2+(r-p)2)


b.ΔPQR is a right angled triangle


c.the points P,Q and R are collinear


d.none of these

Grade:12th Pass

1 Answers

Mera Andaaz
26 Points
3 years ago
1/xp = a + ( p – 1)d
1/xq = a + ( q – 1)d
1/xr  = a + ( r – 1)d
 
Determinant  =  0
 |a + ( p – 1)d    p    1|
 |a + ( q – 1)d    q    1|     =    0
 |a + ( r – 1)d     r     1|
 
Therfore Answer is (c)

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