Home
Class 12
MATHS
If p + q + r = a + b + c = 0, then the d...

If p + q + r = a + b + c = 0, then the determinant `|{:(pa,qb,rc),(qc,ra,pb),(rb,pc,qa):}|` equals

A

`abc|{:(p,q,r),(r,p,q),(q,r,p):}|`

B

`pqr|{:(a,b,c),(c,a,b),(b,c,a):}|`

C

`(a^3+b^3+c^3)(p^3+q^3+r^3)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    FIITJEE|Exercise COMPREHENSIONS -I|3 Videos

  • DETERMINANT

    FIITJEE|Exercise COMPREHENSIONS -II|3 Videos

  • DETERMINANT

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I|53 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

If p + q + r = a + b + c = 0, then the determinant |(pa,qb,rc),(qc,ra,pb),(rb,pc,qa)| equal to :

If p+q+r=0=a+b+c , then the value of the determnalnt |p a q b r c q c r a p b r b p c q a|i s 0 b. p a+q b+r c c. 1 d. none of these

If p+q+r=0 and |(pa,qb,rc),(qc,ra,pb),(rb,pc,qa)| = lambda |(a,b,c),(c,a,b),(b,c,a)| then lambda =

If Delta is the value of the determinant |(a_(1), b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| then what is the value of the following determinant? |(pa_(1), b_(1), qc_(1)),(pa_(2), b_(2), qc_(2)),(pa_(3), b_(3),qc_(3))| (p ne 0 or 1, q ne 0 or 1)

If a,b,c are there given non-coplanar vectors and any arbitrary vector r is in space. Where, Delta_(1) =|{:(r.a,b.a,c.a),(r.b,b.b,a.b),(r.a,b.c,c.c):}|, Delta_(2)=|{:(a.a,r.a,c.a),(a.b,r.b,c.b),(a.c,r.c,c.c):}|, Delta_(3) =|{:(a.a,b.a,r.a),(a.b,b.b,r.b),(a.c,b.c,r.c):}|, Delta=|{:(a.a,b.a,c.a),(a.b,b.b,c.b),(a.c,c.c,c.c):}| The value of |{:(a,b,c),(a.p,b.p,c.p),(a.q,b.q,c.q):}| is:

FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) Level -II
  1. In a set A=(3^3,7^3,11^3,15^3,……) if 9 elements are selected from set ...

    Text Solution

    |

  2. If ai,i=1,2,....,9 are perfect odd squares, then |[a1,a2,a3],[a4,a5,a6...

    Text Solution

    |

  3. If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-...

    Text Solution

    |

  4. If a^2+8b^2+2c^2+2d^2-4ab-4bc-4bd=0 ,then the value of |{:(a,b),(c,d):...

    Text Solution

    |

  5. If ai,i=1,2,....,9 are perfect odd squares, then |[a1,a2,a3],[a4,a5,a6...

    Text Solution

    |

  6. If Deltar=|[2^(r-1),1/(r(r+1)),sin rtheta],[x, y, z],[2^n-1, n/(n+1),(...

    Text Solution

    |

  7. If equations a^2x+b^2y+c^2=0,a^4x+b^4y+c^4=0 and x+y+1=0 are consisten...

    Text Solution

    |

  8. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

    Text Solution

    |

  9. If |{:(a, b, aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c," "0):}|=0 t...

    Text Solution

    |

  10. यदि f(x)=|(0,x-a,x-b),(x-a,0,x-c),(x-b,x-c,0)|, तब :

    Text Solution

    |

  11. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

    Text Solution

    |

  12. The value of x satisfying |{:(x-a,b,c),(a,x+b,c),(a,b,x+c):}|=0 is

    Text Solution

    |

  13. If f(x), g(x) and h(x) are polynomials of degree 4 and |{:(f(x),g(x)...

    Text Solution

    |

  14. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

    Text Solution

    |

  15. If p + q + r = a + b + c = 0, then the determinant |{:(pa,qb,rc),(qc,r...

    Text Solution

    |

  16. If a,b,c are sides of DeltaABC such that |{:(c,bcosB+cbeta,acosA+balph...

    Text Solution

    |

  17. If Delta(x)=|{:(x^2+4x-3,2x+4,13),(2x^2+5x-9,4x+5,26),(8x^2-6x+1,16x-6...

    Text Solution

    |

  18. Let ai^2+bi^2+ci^2=1 (for i=1,2,3) and aiaj+bibj+cicj=0 (i != j;i,j=1...

    Text Solution

    |

  19. Suppose |{:(1+x,x,x^2),(x,1+x,x^2),(x^2,x,1+x):}|=Px^5+Qx^4+Rx^3+Mx^2+...

    Text Solution

    |