Home
Class 12
MATHS
Prove that =|a c c-a +b c b b-c b+c a-b ...

Prove that `=|a c c-a +b c b b-c b+c a-b b-c 0 a-c x y z 1+x+y|=0` implies that `a ,b ,c` are in A.P. or `a ,c ,b` are in G.P.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

Prove that =|1 1 1 a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

If a,b, and c are in G.P then a+b,2b and b+ c are in

If a, b, c are in A.P. then show that 3^(a), 3^(b), 3^(c) are in G.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a,c,e are in GP.

If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in A.P., prove that a, b, c, are in A.P.

If (b+c-a)/a ,(c+a-b)/b ,(a+b-c)/c , are in A.P., prove that 1/a ,1/b ,1/c are also in A.P.

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

If x,y,z are in G.P and a^x=b^y=c^z ,then

Prove that {:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}

If a,b,c are in G.P and a^(1/x) = b^(1/y) = c^(1/z) , prove that x,y,z are in A.P.

CENGAGE-DETERMINANTS-All Questions
  1. If a ,b ,and c are the sides of a triangles andA , B and C are the ang...

    Text Solution

    |

  2. If f(x) is a polynomial of degree <3, prove that |1af(a)//(x-a)1bf(b)/...

    Text Solution

    |

  3. Prove that =|a c c-a +b c b b-c b+c a-b b-c 0 a-c x y z 1+x+y|=0 impli...

    Text Solution

    |

  4. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  5. Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...

    Text Solution

    |

  6. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  7. The product of all values of t , for which the system of equations (a-...

    Text Solution

    |

  8. Prove that for any A.P. a1, a2, a3, , then determinant |ap+a(p+m)+a(p...

    Text Solution

    |

  9. Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1]...

    Text Solution

    |

  10. If =|-x a bb-x a a b-x| , then a factor is a+b+x x^2-(a-b)+x+a^2+b...

    Text Solution

    |

  11. If g(x)=|a^(-x)e^(x loge a)x^2a^(-3x)e^(3x loge a)x^4a^(-5x)e^(5x loge...

    Text Solution

    |

  12. the sum of values of p for which the equations x+y+z=1x+2y +4z=p...

    Text Solution

    |

  13. The value of |alpha| for which the system of equation alphax+y+z=...

    Text Solution

    |

  14. Let D1=|a b a+b c d c+d a b a-b|a n dD2=|a c a+c b d b+d a c a+b+c| th...

    Text Solution

    |

  15. If |xx+y x+y+z2x3x+2y4x+3y+2z3x6x+3y 10 x+6y+3z|=64 , then the real va...

    Text Solution

    |

  16. If =|1 3costheta1s intheta1 3costheta1s intheta1| , then the value of ...

    Text Solution

    |

  17. If |x^n x^(n+2)x^(n+4)y^n y^(n+2)y^(n+4)z^n z^(n+2)z^(n+4)|=(1/(y^2)-1...

    Text Solution

    |

  18. The value of |2x1y1x1y2+x2y1x1y3+x3y1x1y2+x2y1 2x2y2x2y3+x3y2x1y3+x3y1...

    Text Solution

    |

  19. Given A=|a b2c d e2fl m2n|,B=|f2d e2n4l2m c2a b| , then the value of B...

    Text Solution

    |

  20. Number of real roots of the equation[[1, x, x], [ x, 1, x],[ x, ...

    Text Solution

    |