Home
Class 12
MATHS
The value of determinant |{:(a-b,b+c,a),...

The value of determinant `|{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}|` is

A

`a^(3)+b^(3)+c^(3)`

B

`3bc`

C

`a^(3)+b^(3)+c^(3)-3abc`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-II (Fill in the blanks questions)|31 Videos

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-III (True or False questions)|25 Videos

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Example (Questions caryying 6 marks)|35 Videos

  • DEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTION CARRYING 4 MARKS|8 Videos

  • DIFFERENTAL QUATIONS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|41 Videos

Similar Questions

Explore conceptually related problems

If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin B. sin C, then find the valueof determinant |{:(a,b,c),(b,c,a),(c,a,b):}|.

Write the value of the determinant |(0,a-b,a-c), (b-a, 0, b-c),(c-a, c-b, 0)|

Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c):} .

Without expanding, prove that the following determinants vanish: {:|(a,b,a+b),(b,c,b+c),(c,a,c+a)|

Evaluate the following determinants: |(0,c,b),(c,0,a),(-b,-a,0)|

Evaluate the following: {:|(b+c,a,a),(b,c+a,b),(c,c,a+b)|

If a, b, c are positive and unequal, show that value of the determinant triangle = |[a,b,c],[b,c,a],[c,a,b]| is negative.

Without actual expansion, prove that the following determinants vanish: {:|(a,b,c),(a-b,b-c,c-a),(b,c,a)|

ACCURATE PUBLICATION-DETERMINANTS-Type-I (Multiple choice questions)
  1. If A=[{:(3,1),(1,2):}], then A(adjA) equals

    Text Solution

    |

  2. If A = ([4,3],[3,4]), then A (Adj A) equals :

    Text Solution

    |

  3. If A=[(3,2),(1,4)] , then A(adj A) equals

    Text Solution

    |

  4. The inverse of a symmetric matrix is :

    Text Solution

    |

  5. Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

    Text Solution

    |

  6. If x,y in R then the determinant Delta=|{:(cosx,-sinx,1),(sinx,cosx,1)...

    Text Solution

    |

  7. If |(2x,5),(8,x)|=|(6,-2),(7,3)| , write the value of x.

    Text Solution

    |

  8. The value of determinant |{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}| is

    Text Solution

    |

  9. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

    Text Solution

    |

  10. The determinant |{:(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ca...

    Text Solution

    |

  11. The number of distinct real roots of |{:(sinx,cosx,cosx),(cosx,sinx,co...

    Text Solution

    |

  12. If A,B and C are angles of a triangle, then the determinant: {:|(-1,...

    Text Solution

    |

  13. Let f(t)=|{:(cost,t,1),(2sint,t,2t),(sint,t,t):}|, then LT(t to o)(f(t...

    Text Solution

    |

  14. Find the maximum value of : {:|(1,1,1),(1,1+sintheta,1),(1,1,1+costh...

    Text Solution

    |

  15. Consider the determinant f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2...

    Text Solution

    |

  16. If A=[{:(2,lambda,-3),(0,2,5),(1,1,3):}| , then A^(-1) exists if

    Text Solution

    |

  17. If A and B are invertibel , then which of the following is not correct

    Text Solution

    |

  18. If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1...

    Text Solution

    |

  19. Without expanding, prove the following |(x,x+y,x+2y),(x+2y,x,x+y),(...

    Text Solution

    |

  20. There are two values of a which makes determinant, Delta=|{:(1,-2,5),(...

    Text Solution

    |