Home
Class 12
MATHS
if bc+ qr= ca+rp = ab+ pq =-1 then prov...

if `bc+ qr= ca+rp = ab+ pq =-1` then prove that
`|{:(ap,,a,,p),(bq,,b,,q),(cr,,c,,r):}|=0`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Expansion of Determinant|5 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Single Option Correct Type Questions|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

If bc+qr=ca+rp=ab+pq=-1 and (abc,pqr!=0) then |[ap,a,p],[bq,b,q],[cr,c,r]| is (A) 1 (B) 2 (C) 0 (D) 3

If p^(th), q^(th),r^(th) terms an A.P are 1/a,1/b and 1/c respectively prove that Delta=|(bc,ca,ab),(p,q,r),(1,1,1)|=0

Without expanding at any state, prove that |((1)/(a),a,bc),((1)/(b),b,ca),((1)/(c ),c,ab)|=0

Without expanding at any state, prove that |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))|=0

If AB=QR , BC=PR and CA=PQ then

If a,b,c are in H.P and ab+bc+ca=15 then ca=

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 are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

The sums of first p, q, r terms of an A.P. are a, b, c respectively. Prove that (a)/(p) (q-r) +(b)/(q) (r-p) +(c )/(r) (p-q) =0

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. if bc+ qr= ca+rp = ab+ pq =-1 then prove that |{:(ap,,a,,p),(bq,,b...

    Text Solution

    |

  2. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

    Text Solution

    |

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

    Text Solution

    |

  4. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k for which the linear equations 4x+ky+2...

    Text Solution

    |

  11. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  12. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  13. if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

    Text Solution

    |

  14. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

    Text Solution

    |

  17. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  18. Let alpha, lambda , mu in R.Consider the system of linear equations ...

    Text Solution

    |

  19. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |