Home
Class 12
MATHS
Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c...

Evaluate: `|(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)|` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^2)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are hon coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are non coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Without expanding the determinant, prove that |(a,a^2,bc),(b,b^2,ca),(c,c^2,ab)|=|(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3)|

Without expanding determinant at any stage evaluate |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

Evaluate the following |(1, 1, 1),(a^2,b^2,c^2),(a^3,b^3,c^3)|

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove that: |-a^2 ab ac ba -b^2 bc ...

    Text Solution

    |

  2. Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

    Text Solution

    |

  3. Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)| .

    Text Solution

    |

  4. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

    Text Solution

    |

  5. Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,g...

    Text Solution

    |

  6. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

    Text Solution

    |

  7. In a A B C ,if|1 1 1 1+cosA 1+cosB 1+cosC cos^2A+A cos^2B+cosB cos^2...

    Text Solution

    |

  8. Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,...

    Text Solution

    |

  9. If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove th...

    Text Solution

    |

  10. For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z...

    Text Solution

    |

  11. Using properties of determinants, show that |1 a a^2 -b c 1 b ...

    Text Solution

    |

  12. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

    Text Solution

    |

  13. Let a ,\ b and c denote the sides B C ,\ C A and A B respectively of ...

    Text Solution

    |

  14. If f(x)=|[a-1, 0,a] , [x,a-1,a], [x^2a, x, a]| , using properties of ...

    Text Solution

    |

  15. Show that: x p q p x q q q xx-p)(x^2+p x-2q^2) .

    Text Solution

    |

  16. If m in N and mgeq2 prove that: |1 1 1\ ^m C1\ ^(m+1)C1\ ^(m+2)C1\ ^m...

    Text Solution

    |

  17. Evaluate: =|10 ! 11 ! 12 ! 11 ! 12 ! 13 ! 12 ! 13 ! 14 !|

    Text Solution

    |

  18. Prove that: |x+yx x5x+4y4x2x 10 x+8y8x3x|=x^3 .

    Text Solution

    |

  19. Show that: |[1 ,1+p,1+p+q],[2, 3+2p,1+3p+2q],[3, 6+3p,1+6p+3q]|=1 .

    Text Solution

    |

  20. Show that: |[a, a+b ,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]...

    Text Solution

    |