Home
Class 12
MATHS
If |[a^2+lambda^2,ab+clambda,ca-blambda]...

If `|[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+aλ],[ca+blambda,bc-alambda,c^2+lambda^2]|``|[λ,c,-b],[-c,λ,a] ,[b,-a,λ]|`=`(1+a^2+b^2+c^2)^3` , then he value of `lambda` is `8` b. `27` c. `1` d. `-1`

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

|[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|=|[a,b,c],[b,c,a],[c,a,b]|^2

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to :

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

If the points A(lambda, 2lambda), B(3lambda,3lambda) and C(3,1) are collinear, then lambda=

Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

Show that |[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,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to : (A) 4 lambda abc (B) -4 lambda abc (C) 4 lambda^2 (D) -4 lambda^2

If b-c,2b-lambda,b-a " are in HP, then " a-(lambda)/(2),b-(lambda)/(2),c-(lambda)/(2) are is

If a,b,c are in AP and (a+2b-c)(2b+c-a)(c+a-b)=lambdaabc , then lambda is

If a,b, c, lambda in N , then the least possible value of |(a^(2)+lambda, ab,ac),(ba,b^(2)+lambda,bc),(ca, cb, c^(2)+lambda)| is

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c...

    Text Solution

    |

  2. Let alpha be a repeated root of a quadratic equation f(x)=0 and A(x...

    Text Solution

    |

  3. If |[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+a...

    Text Solution

    |

  4. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

    Text Solution

    |

  5. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

    Text Solution

    |

  6. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

    Text Solution

    |

  7. Prove that the value of each the following determinants is zero: |a...

    Text Solution

    |

  8. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

    Text Solution

    |

  9. The value of determinant |[ ^n C(r-1), ^n Cr, (r+1)^(n+2)C(r+1)],[ ^n...

    Text Solution

    |

  10. Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the va...

    Text Solution

    |

  11. If the determinant |b-cc-a a-bb^(prime)-c ' c^(prime)-a ' a^(prime)-b ...

    Text Solution

    |

  12. Let a ,b , c be the real numbers. The following system of equations in...

    Text Solution

    |

  13. The value of the determinant |(sintheta, costheta, sin2theta) , (sin(t...

    Text Solution

    |

  14. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

    Text Solution

    |

  15. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |

  16. Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B...

    Text Solution

    |

  17. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

    Text Solution

    |

  18. Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b...

    Text Solution

    |

  19. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

    Text Solution

    |

  20. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

    Text Solution

    |