Home
Class 12
MATHS
Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^...

Prove that `|(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|=` `|(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|= 2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)|=(x-y)(y-z)(z-x)

Prove that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0

|((x+1/x)^(2),(x-1/x)^(2),1),((y+1/y)^(2),(y-1/y)^(2),1),((z+1/z)^(2),(z-1/z)^(2),1)|

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

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

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

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

Show that {:|(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|:} =0

If x + y + z = xyz, then prove that (2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2)) .

CENGAGE-DETERMINANTS-All Questions
  1. Prove that |a1alpha1+b1beta1a1alpha2+b2beta2a1alpha3+b1beta3a2alpha1+b...

    Text Solution

    |

  2. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value...

    Text Solution

    |

  3. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

    Text Solution

    |

  4. If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^...

    Text Solution

    |

  5. If |x^n x^(n+2)x^(n+3)y^n y^(n+2)y^(n+3)z^n z^(n+2)z^(n+3)|=(x-y)(y-z)...

    Text Solution

    |

  6. Solve the system of the equations: a x+b y+c z=d a^2x+b^2y+c^2z=d^2 a^...

    Text Solution

    |

  7. if |{:(a,,b-c,,c+b),(a+c,,b ,,c-a),(a-b,,a+b,,c):}|=0 then the line ...

    Text Solution

    |

  8. If 2a x-2y+3z=0,x+a y+2z=0,a n d2+a z=0 have a nontrivial solution,...

    Text Solution

    |

  9. If |.| denotes the greatest integer less than or equal to the real num...

    Text Solution

    |

  10. if (x) =a +bx+cx^(2)" and " alpha, beta gamma are the roots of the ...

    Text Solution

    |

  11. If x ,ya n dz are not all zero and connected by the equations a1x+b...

    Text Solution

    |

  12. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

    Text Solution

    |

  13. If p ,q ,r are in A.P. then value of determinant |a^2+2^(n+1)+2p b^2+2...

    Text Solution

    |

  14. For what values of k , the following system of equations possesses ...

    Text Solution

    |

  15. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

    Text Solution

    |

  16. Solve by Cramers rule x+y+z=6 x-y+z=2 3x+2y-4z=-5

    Text Solution

    |

  17. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

    Text Solution

    |

  18. Find the value of aa n db if the system of equation a^2x-b y=a^2-ba...

    Text Solution

    |

  19. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

    Text Solution

    |

  20. f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)(xvec0)(f(x))/x ...

    Text Solution

    |