Home
Class 12
MATHS
The value of determinant |[b c-a^2,a c-b...

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

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

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

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.

If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

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

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

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)(c- a)

If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^2c^2, then the value of k is a b c b. a^2b^2c^2 c. b c+c a+a b d. none of these

Show that , |[(a^2+b^2)/c,c,c],[a,(b^2+c^2)/a,a],[b,b,(c^2+a^2)/b]|=4abc

Using properties of determinant prove that |[a+b+c,-c,-b],[-c, a+b+c,-a],[-b,-a, a+b+c]|=2(a+b)(b+c)(c+a)

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. 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

    |

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

    Text Solution

    |

  3. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Text Solution

    |

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

    Text Solution

    |

  8. 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

    |

  9. If the determinant |[b-c,c-a, a-b],[b^(prime)-c ', c^(prime)-a ', a^(p...

    Text Solution

    |

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

    Text Solution

    |

  11. By using properties of determinats. Prove that- |(sintheta,costheta,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. 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

    |

  17. If (x)=|(alpha+x,theta+x,lambda+x),(beta+x,varphi+x,mu+x),(gamma+x,psi...

    Text Solution

    |

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

    Text Solution

    |

  19. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

    Text Solution

    |

  20. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

    Text Solution

    |