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

Prove that `|{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)(a+y),,(a+y)(b+y)),((b+z)(c+z),, (c+z)(a+z),,(a+z)(b+x)):}|`
`= (b-c) (c-a) (a-b) (y-z) (z-x) (x-y)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

prove that, |{:(x,b,c),(a,y,c),(a,b,z):}|=(x-a)(y-b)(z-c)((x)/(x-a)+(y)/(y-b)+(z)/(z-c)-2)

Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) , ((c-x)^2,(c-y)^2, (c-z)^2)) = 2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,b,,c),(x,,y,,z),(yz,,xz,,xy):}|

If x/(b + c -a) = y/(c + a - b) = z/(a + b -c) , then show that (b -c) x + (c-a) y + (a -b) z = 0 .

Show that abs((a,b,c),(a+2x,b+2y,c+2z),(x,y,z)) =0

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b)^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a y]|=x y z|[a, b, c],[c ,a ,b],[b ,c ,a]|

If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^(c-a).z^(a-b) = 1 .

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b+c).y^(c+a).z^(a+b) = 1

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. The determinant |[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']| is equal ...

    Text Solution

    |

  2. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

    Text Solution

    |

  3. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

    Text Solution

    |

  4. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

    Text Solution

    |

  5. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

    Text Solution

    |

  6. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

    Text Solution

    |

  7. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of de...

    Text Solution

    |

  8. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

    Text Solution

    |

  9. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

    Text Solution

    |

  10. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

    Text Solution

    |

  11. Which of the following has/have value equal to zero? |[8, 2, 7],[ 12, ...

    Text Solution

    |

  12. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  13. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

    Text Solution

    |

  14. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

    Text Solution

    |

  15. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

    Text Solution

    |

  16. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

    Text Solution

    |

  17. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

    Text Solution

    |

  18. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

    Text Solution

    |

  19. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

    Text Solution

    |

  20. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

    Text Solution

    |