Home
Class 12
MATHS
Using the properties of determinants, pr...

Using the properties of determinants, prove that following `|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

evaluate: |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

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

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

Using properties of determinants, prove the following : |[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)

Using properties of determinants, prove that |{:(,a,b,b+c),(,c,a,c+a),(,b,c,a+b):}|=(a+b+c) (a-c)^2

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

    Text Solution

    |

  2. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

    Text Solution

    |

  3. Using the properties of determinants, prove that following |(a-b-c,2a,...

    Text Solution

    |

  4. If a1,a2,a3,.....an.... are in G.P. then the determinant 'Delta=|[loga...

    Text Solution

    |

  5. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

    Text Solution

    |

  6. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

    Text Solution

    |

  7. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

    Text Solution

    |

  8. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

    Text Solution

    |

  9. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

    Text Solution

    |

  10. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

    Text Solution

    |

  11. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

    Text Solution

    |

  12. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

    Text Solution

    |

  13. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

    Text Solution

    |

  14. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

    Text Solution

    |

  15. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

    Text Solution

    |

  16. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

    Text Solution

    |

  17. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

    Text Solution

    |

  18. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

    Text Solution

    |

  19. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

    Text Solution

    |

  20. If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...

    Text Solution

    |