Home
Class 12
MATHS
Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+...

Prove that `abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c],[p,q,r],[x,y,z]]`

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION SET

    USHA PUBLICATION|Exercise MODEL QUESTION SET|692 Videos

  • PREVIOUS YEAR QUESTION 2016

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |44 Videos

Similar Questions

Explore conceptually related problems

Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2[[a,b,c],[p,q,r],[x,y,z]]

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]

Simplify: "[x y z]"xx[[a,h,g],[h,b,f],[g,f,c]]xx[[x],[y],[z]]

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

Using properties of the determinants, prove that: |[2y, y-z-x, 2y],[2z, 2z, z-x-y], [x-y-z, 2x, 2x]| = (x+y+z)^3

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]]

Express as a sum of a symmetric and a skew symmetric matrix: [[x,a,b],[a,y,c],[b,c,z]]

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

USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

    Text Solution

    |

  2. A diet for a sick person must contain at least 4000 units of vitamins,...

    Text Solution

    |

  3. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

    Text Solution

    |

  4. Find inverse of the following matrices by elementary row/column operat...

    Text Solution

    |

  5. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

    Text Solution

    |

  6. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

    Text Solution

    |

  7. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

    Text Solution

    |

  8. Test differentiability and continuity of the following functions. |1...

    Text Solution

    |

  9. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

    Text Solution

    |

  10. Find dy/dx if y = x cot^(-1) (x/y)

    Text Solution

    |

  11. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

    Text Solution

    |

  12. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

    Text Solution

    |

  13. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

    Text Solution

    |

  14. int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)

    Text Solution

    |

  15. Find the area of the region bounded by y=6x-x^2x-axis and between ordi...

    Text Solution

    |

  16. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

    Text Solution

    |

  17. From a differential equation from the equation y=ae^(2x)+be^(-x) by el...

    Text Solution

    |

  18. Prove the following by vector method. An angle inscribed in a semi-cir...

    Text Solution

    |

  19. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

    Text Solution

    |

  20. If the sum of two unit vectors is a unit vector, show that the magnitu...

    Text Solution

    |