Home
Class 12
MATHS
Prove that |[a-b-c,2a,2a],[2b, b-c-a, 2b...

Prove that `|[a-b-c,2a,2a],[2b, b-c-a, 2b],[2c, 2c, c-a-b]|= (a+b+c)^3`.

Text Solution

Verified by Experts

The correct Answer is:
`(a+b+c)^(3)`
Promotional Banner

Topper's Solved these Questions

  • CHSE ODISHA EXAMINATION PAPER - 2018

    ARIHANT PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS (ANSWER ANY THREE QUESTIONS)|38 Videos

  • AREA UNDER PLANE CURVES

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANWER TYPE QUESTIONS)|15 Videos

  • CHSE ODISHA EXAMINATION PAPER 2019

    ARIHANT PUBLICATION|Exercise Group C (30 Marks) |13 Videos

Similar Questions

Explore conceptually related problems

Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Prove that: |[a+b+2c, a, b],[c, b+c+2a, b],[c, a, c+a+2b]|=2(a+b+c)^3

Prove that: |[a, b, c],[a-b, b-c, c-a ], [b+c, c+a, a+b]|= a^3+b^3+c^3-3abc

Prove that: 1/(bc+ca+ab)|[a, b, c],[a^2, b^2, c^2], [bc, ca, ab]|=(b-c),(c-a),(a-b)

Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]] =4ab

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

ARIHANT PUBLICATION-CHSE ODISHA EXAMINATION PAPER - 2018 -SHORT ANSWER TYPE QUESTIONS (ANSWER ANY THREE QUESTIONS)
  1. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

    Text Solution

    |

  2. Find the inverse of the following matrix [{:(1,1,2),(0,1,2),(1,2,1):}]...

    Text Solution

    |

  3. Prove that |[a-b-c,2a,2a],[2b, b-c-a, 2b],[2c, 2c, c-a-b]|= (a+b+c)^3.

    Text Solution

    |

  4. Show that the sum of the intercepts on the coordinate axes of any tang...

    Text Solution

    |

  5. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

    Text Solution

    |

  6. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

    Text Solution

    |

  7. Differentiate y=(siny)^(sin2x)

    Text Solution

    |

  8. Test the continuity of the following function at x=0 f(x)={{:((1-e^(...

    Text Solution

    |

  9. From the differential equation whose general solution is y=asint+be^t.

    Text Solution

    |

  10. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

    Text Solution

    |

  11. Evaluate int (dx)/((x+1)sqrt(1-x^2))

    Text Solution

    |

  12. int(0)^(1/2)(1)/(sqrt(1-x^(2)))dx.

    Text Solution

    |

  13. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

    Text Solution

    |

  14. Prove that the measure of the angle between two main diagonals of a cu...

    Text Solution

    |

  15. The position vectors of two points A and B are 3hati+hatj+2hatk and ha...

    Text Solution

    |

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

    Text Solution

    |

  17. Prove that [(veca+vecb,vecb+vecc,vecc+veca)]=2[(veca,vecb,vecc)].

    Text Solution

    |

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

    Text Solution

    |

  19. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

    Text Solution

    |

  20. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

    Text Solution

    |