Home
Class 12
MATHS
If a , b , c are all positive and are p ...

If `a , b , c` are all positive and are `p t h ,q t ha n dr t h` terms of a G.P., then that `=|loga p1logb q1logc r1|=0`

Text Solution

Verified by Experts

`a -> pth`
`b -> qth`
`c -> rth`
`a = AR^(P-1)`
`b= AR^(q-1)`
`c =AR^(r-1)`
`log a = log A + (p-1)log R`
`log b = log A + (q-1)log R`
...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

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 are positive and ar the p^(th),q^(th),r^(th) terms respectively of a G.P show that, |{:(,log a,p,1),(,log b,q,1),(,log c,r,1):}|=0

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

If the positive numbers a, b and c are the pth, qth and rth terms of GP, then the vectors (loga) hati+(logb) hatj+(logc) hatk and (q-r)hati+(r-p)hatj+(p-q) hatk are

Suppose a, b, c gt 0 and are respectively the pth, qth and rth terms of a G.P. Let x=(loga)i+(logb)j+(logc)k y=(q-r)i+(r-p)j+(p-q)k If angle between x and y is kpi , then k = ______

l, m,n are the p^(th), q ^(th) and r ^(th) term of a G.P. all positive, then |{:(logl, p, 1),(log m, q, 1),(log n ,r,1):}| equals :

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Solve : |(x-2, 2x-3, 3x-4), (x-4, 2x-9, 3x-16) ,(x-8 ,2x-27,3x-64)|=0

    Text Solution

    |

  2. If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y ...

    Text Solution

    |

  3. If a , b , c are all positive and are p t h ,q t ha n dr t h terms of ...

    Text Solution

    |

  4. Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-...

    Text Solution

    |

  5. |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|...

    Text Solution

    |

  6. Prove that : |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|...

    Text Solution

    |

  7. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

    Text Solution

    |

  8. Prove that: |[a, b, ax+by],[ b, c, bx+cy], [ax+by, bx+cy,0]|=(b^2-a c)...

    Text Solution

    |

  9. Without expanding the determinant, show that (a+b+c) is a factor of th...

    Text Solution

    |

  10. If m in N and mgeq2, prove that: |1 1 1m(C1)m+1(C1)m+2(C1)m(C2)m+1(C2...

    Text Solution

    |

  11. Evaluate: =|10 ! 11 ! 12 ! 11 ! 12 ! 13 ! 12 ! 13 ! 14 !|

    Text Solution

    |

  12. Show that: |b+cc+a a+b q+r r+p p+q y+z z+xx+y|=2|a b c p q r x y z|

    Text Solution

    |

  13. Prove that |(1+a,1, 1),( 1,a+b,1),( 1, 1, 1+c)|=a b c(a+1/a+1/b+1/c)=a...

    Text Solution

    |

  14. If a , b , c , are roots of the equation x^3+p x+q=0, prove that |[a...

    Text Solution

    |

  15. If a+b+c!=0 and |(a, b, c),(b, c, a),(c,a,b)|=0 , then prove that a=b=...

    Text Solution

    |

  16. Let a , band c detnote the sides BC,CA andAB respectively of triangl...

    Text Solution

    |

  17. Prove that |[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3

    Text Solution

    |

  18. Using properties of determinant show that: |[1 , a , -bc] , [1 , b , -...

    Text Solution

    |

  19. In a A B C ,if|(1 ,1 ,1),( 1+cosA,1+cosB,1+cosC),(cos^2A+cosB,cos^2A+...

    Text Solution

    |

  20. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

    Text Solution

    |