Home
Class 12
MATHS
Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c...

Show that: `|[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)dot`

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

{:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)

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

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

|{:(" "3a," "-a+b,-a+c),(a-b," "3b," "c-b),(a-c," "b-c," "3c):}|=3(a+b+c)(ab+bc+ca)

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

If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|=0, show that a b c(a b+b c+c a)=a+b+c

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

Show that abs((a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)) = a^3+b^3+c^3 -3abc.

Show that, |{:(" "a,b-c,c+b),(a+c," "b,c-a),(a-b,b+a," "c):}|=(a+b+c)(a^2+b^2+c^2)

|{:(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c):}|=

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

    Text Solution

    |

  2. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  3. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

    Text Solution

    |

  4. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

    Text Solution

    |

  5. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

    Text Solution

    |

  6. The value of |y z z xx y p2p3r1 1 1|,w h e r ex ,y ,z are respectively...

    Text Solution

    |

  7. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

    Text Solution

    |

  8. Prove that the value of each the following determinants is zero: |s...

    Text Solution

    |

  9. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

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

    Text Solution

    |

  11. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

    Text Solution

    |

  12. Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m ...

    Text Solution

    |

  13. Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]|=2(a-b)(b...

    Text Solution

    |

  14. If =|sin theta cos var phi sin theta sin var phi cos theta cos theta c...

    Text Solution

    |

  15. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)no so...

    Text Solution

    |

  16. Show that if x1, x2, x3!=0 abs((x1+a1.b1,a1.b2,a1.b3),(a2.b1,x2+a2.b...

    Text Solution

    |

  17. If determinant |[cos(theta+phi),-sin(theta+phi),cos2phi],[sin theta,co...

    Text Solution

    |

  18. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

    Text Solution

    |

  19. The values of k in R for which the system of equations x+k y+3z=0,k x...

    Text Solution

    |

  20. A determinant of second order is made with the elements 0 and 1. Fi...

    Text Solution

    |