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

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)`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|401 Videos

  • PROBABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|467 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

Prove that: {:|(1,1,1),(a,b,c),(bc,ca,ab)| = (a-b)(b-c)(c-a)

Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2),c^(2)),( bc,ca,ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a)

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

Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,ca,ab)|=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove that: {:|(bc,a,1),(ca,b,1),(ab,c,1)| = (a-b)(b-c)(a-c)

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

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)

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. If A = (a,b,c,d) and f corresponds to the subset (a,b),(b,d),(c,a),(d,...

    Text Solution

    |

  2. If g={(1,1),(2,3),(3,5),(4,7)} is a function described by the formula ...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f : R rarr R be defined by f(x) = 1/x AA x inR, then f is

    Text Solution

    |

  5. If f : R rarr R is defined by f(x) = x^2 - 3x + 2, find f(f(x)).

    Text Solution

    |

  6. If f. g : R rarr R are defined respectively as f(X) = 2x + 1 and g (x)...

    Text Solution

    |

  7. Are the following sets of ordered pairs functions? (x,y) : x is a pers...

    Text Solution

    |

  8. Are the following sets of ordered pairs functions? (a,b), a is a pers...

    Text Solution

    |

  9. If f(x) = x + 7 and g(x) = x - 7 , x in R find (fog) (7).

    Text Solution

    |

  10. The range of function f(x)= abs(x-1)/(x-1)

    Text Solution

    |

  11. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6...

    Text Solution

    |

  12. If f(x) = x^2 and g (x) = 2x + 3, then the laue of gof (-1) is

    Text Solution

    |

  13. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

    Text Solution

    |

  14. Let f(x) = x^2 and g (x) = sqrtx, then (fog) (x) = x for all x in D(fo...

    Text Solution

    |

  15. Let '*' be the binary operation defined on N by the rule a * b = 3 a +...

    Text Solution

    |

  16. Is the binary operation '*' defined on Z (set of integers) by the rule...

    Text Solution

    |

  17. Let '*' be the operation defined on the set Z of integers by the rule ...

    Text Solution

    |

  18. Let '*' be the binary operation defined on Q by the rule a * b = ab^2 ...

    Text Solution

    |

  19. Let '*' be the binary operaton on the set (1,2) defined by the followi...

    Text Solution

    |

  20. Let '*' be the binary operation defined on the set R - (0) by the rule...

    Text Solution

    |