Home
Class 12
MATHS
Prove that : {:|(a^2a^2-(b-c)^2,bc),(b^2...

Prove that : `{:|(a^2a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b)^2,ab)| = (b-c)(c-a)(a-b)(a+b+c)(a^2+b^2+c^2)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b+c)^3

Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b-c)(c-a)

The determinant |{:(a^(2),a^(2)-(b-c)^(2),bc),(b^(2),b^(2)-(c-a)^(2),ca),(c^(2),c^(2)-(a-b)^(2),ab):}| is divisible by

Prove that |{:((b+c)^(2), a^(2), bc),((c+a)^(2), b^(2), ca),((a+b)^(2), c^(2), ab):}|= (a-b) (b-c)(c-a)(a + b+c) (a^(2) + b^(2) + c^(2)) .

Prove that: {:|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,)|=(a+b)+c)(a^2+b^2+c^2)

Prove that |{:(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b^(2)):}| = 4a^(2)b^(2)c^(2)

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^2

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

    Text Solution

    |

  2. Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3.

    Text Solution

    |

  3. Prove that : {:|(a^2a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b...

    Text Solution

    |

  4. If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),...

    Text Solution

    |

  5. Using determinant , find the area of triangle with verticles (1,0) ,...

    Text Solution

    |

  6. Using determinants find the area of triangle with vertices (1,-1), ...

    Text Solution

    |

  7. Find the area of the triangle with vertices at the points given in eac...

    Text Solution

    |

  8. Find area of the triangle with vertices at the point given in the fol...

    Text Solution

    |

  9. Find area of the triangle with vertices at the point given in the fol...

    Text Solution

    |

  10. Using determinants, show that the following points are collinear: (1...

    Text Solution

    |

  11. Using determinants, show that the following points are collinear: (-...

    Text Solution

    |

  12. If the point (3,-2),(x,2),(8,8) are collinear, find 'x' using determin...

    Text Solution

    |

  13. if area of triangle is 35sq.unit with vertices (2,-6) (5,4) and (K,4) ...

    Text Solution

    |

  14. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

    Text Solution

    |

  15. Determine the value of 'x' for which the area of the triangle formed b...

    Text Solution

    |

  16. Find equation of line joining (1, 2) and (3, 6) using determinants.

    Text Solution

    |

  17. Find equation of line joining (3, 1) and (9, 3) using determinants.

    Text Solution

    |

  18. Find the equation of the line joining A(1, 3) and B (0, 0) using deter...

    Text Solution

    |

  19. Prove that area of the trianlge whose vertices are (at1^2,2at1) , (at2...

    Text Solution

    |

  20. Prove that the (a, b+c), (b, c+a) and (c, a+b) are collinear.

    Text Solution

    |