If P&equiv;(1/xp,p);Q&equiv;(1/xq,q);R&equiv;(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

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Analytical Geometry> straight lines...

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)={(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

Menka Malguri , 14 Years ago

Grade 12th Pass

1 Answers

Mera Andaaz

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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Analytical Geometry> straight lines...

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

Menka Malguri , 14 Years ago

Mera Andaaz

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