Home
Class 12
MATHS
Let a ,b ,c be positive and not all equa...

Let `a ,b ,c` be positive and not all equal. Show that the value of the determinant `|[a, b, c],[b, c, a],[ c, a ,b]|` is negative.

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

If, a,b,c are positive and unequal,show that value of the determinant Delta ={:|( a,b,c),( b,c,a),( c,a,b)|:} is negative

Show that the points (a,b+c),(b,c+a) and (c,a+b) are collinear.

If a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

Show that A sub B then C- B sub C- A

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 c-a^2],[a b-c^2,b c-a^2,a c-b^2]| is a. always positive b. always negative c. always zero d. cannot say anything

If a,b,c are positive real number, then the least value of (a+b+c)(1/a+1/b+1/c) is

If a,b,c are integers not all simultaneously equal, then the minimum value of |a+ b omega + c omega ^(2)| is-

Using determinant : Show that the points (a,b+c),(b,c+a) and (c,a+b) are collinear .

Let a ,b , c be positive integers such that (b)/(a) is an integer . If a , b , c are in geometric progression and the arithmetic mean of a , b , c , is b + 2 , then value of (a^(2)+a-14)/(a+1)

Let a, b , c be positive integers such that b/a is an integer. if a, b , c are in geometric progression and the arithmetic mean of a , b , c is b + 2, then the value of (a^2 + a -14)/(a + 1) is

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Find the value of lambda for which the homogeneous system of equations...

    Text Solution

    |

  2. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

    Text Solution

    |

  3. Let a ,b ,c be positive and not all equal. Show that the value of the ...

    Text Solution

    |

  4. if f(x)=|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)...

    Text Solution

    |

  5. Without expanding a determinant at any stage, show that abs((x^2+x ,x+...

    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. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

    Text Solution

    |

  8. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

    Text Solution

    |

  9. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

    Text Solution

    |

  10. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

    Text Solution

    |

  11. Consider the system linear equations in x ,y ,a n dz given by (sin3the...

    Text Solution

    |

  12. If alpha,beta "and" gamma are real number without expanding at any sta...

    Text Solution

    |

  13. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

    Text Solution

    |

  14. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

    Text Solution

    |

  15. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

    Text Solution

    |

  16. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value o...

    Text Solution

    |

  17. Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) ...

    Text Solution

    |

  18. If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value ...

    Text Solution

    |

  19. If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z...

    Text Solution

    |

  20. Solve the system of the equations: a x+b y+c z=d, a^2x+b^2y+c^2z=d^2,...

    Text Solution

    |