Home
Class 12
MATHS
Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, ...

Evaluate `|{:(0,c,b),(c,0,a),(b,a,0):}|`, hence show that .
`|{:(0,c,b),(c,0,a),(b,a,0):}|^2=|{:(b^2+c^2," "ab," "ac),(" "ab,c^2+a^2," "bc),(" "ca," "bc,a^2+b^2):}|=4a^2b^2c^2`

Text Solution

Verified by Experts

The correct Answer is:
2abc
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CHHAYA PUBLICATION|Exercise EXERCISE 2C|37 Videos

  • DETERMINANT

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Multiple Correct Answers Type)|5 Videos

  • DETERMINANT

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|36 Videos

  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Evalute |{:(0,c,b),(c,0,a),(b,a,0):}| and hence show that, |{:(" "-a^2," "ab," "ac),(" "ab," "-b^2," "bc),(" "ca," "bc," "-c^2):}|=4a^2b^2c^2

|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2):}|=4a^2b^2c^2

Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lambdaa^2b^2c^2, then find the value of lambda

Using properties of determinants , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc) and hence show that, |{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

Show that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ca,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2)

|{:(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,cb^2,0):}|=2a^3b^3c^3

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|=|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|

Prove that, abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)) =4 a^2b^2c^2 .

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. |{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|

    Text Solution

    |

  2. If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , p...

    Text Solution

    |

  3. Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, hence show that . |{:(0,c,b)...

    Text Solution

    |

  4. Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...

    Text Solution

    |

  5. prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...

    Text Solution

    |

  6. Prove that , the value of the determinant |{:(x+1,x+2,x+4),(x+3,x+5,...

    Text Solution

    |

  7. |{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc

    Text Solution

    |

  8. |{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...

    Text Solution

    |

  9. |{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...

    Text Solution

    |

  10. |{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)

    Text Solution

    |

  11. |{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3

    Text Solution

    |

  12. |{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...

    Text Solution

    |

  13. |{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...

    Text Solution

    |

  14. |{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...

    Text Solution

    |

  15. |{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...

    Text Solution

    |

  16. prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...

    Text Solution

    |

  17. If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...

    Text Solution

    |

  18. If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...

    Text Solution

    |

  19. without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...

    Text Solution

    |

  20. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

    Text Solution

    |