Home
Class 12
MATHS
Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a...

Prove that : `|{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(3)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4c|7 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4d|13 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4a|6 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

Similar Questions

Explore conceptually related problems

Prove that : |{:(a,b,c),(b,c,a),(c,a,b):}|=3 a b c-a^(3)-b^(3)-c^(3)

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

Prove: \ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^3

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+b^3+c^3-3a b c

Prove that : (a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)=2(a^3+b^3+c^3-3a b c)

Prove that : (a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)=2(a^3+b^3+c^3-3a b c)

Prove: |[a+b+2c, a, b], [c, b+c+2a, b], [c ,a ,c+a+2b]|=2(a+b+c)^3

Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Exercise 4b
  1. Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-...

    Text Solution

    |

  2. Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}|=(x-y)(y-z)(z-x)...

    Text Solution

    |

  3. Prove that : |{:(x+a,x,x),(x,x+a,x),(x,x,x+a):}|=a^(2)(3x+a)

    Text Solution

    |

  4. Prove that : |{:(x+a,b,c),(a,x+b,c),(a,b,x+c):}|=x^(2)(x+a+b+c)

    Text Solution

    |

  5. Prove that : |{:(x-y-z ,2x, 2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|=(x+y+z)...

    Text Solution

    |

  6. Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+z+2y):}|=2(x+y+z)^(3)

    Text Solution

    |

  7. Using the properties of determinants, prove that |{:((y+z)^(2)," "x...

    Text Solution

    |

  8. Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(...

    Text Solution

    |

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

    Text Solution

    |

  10. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

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

    Text Solution

    |

  12. Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0

    Text Solution

    |

  13. |[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]|=0

    Text Solution

    |

  14. Solve the equation |{:(x+a,x+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0

    Text Solution

    |

  15. One root of the equation |(3x-8, 3, 3),(3,3x-8, 3),(3,3,3x-8)|=0 is ...

    Text Solution

    |

  16. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

    Text Solution

    |

  17. If the sides of a DeltaABC are a, b, c and |{:(a^(2),b^(2),c^(2)),((a+...

    Text Solution

    |

  18. If the pth, qth and rth terms of a G.P, are x,y and z repectively, the...

    Text Solution

    |

  19. Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(z-x)...

    Text Solution

    |

  20. Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

    Text Solution

    |