Home
Class 12
MATHS
The value of the determinant |(k a, k^2+...

The value of the determinant `|(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c, k^2+c^2, 1)|` is (A) `k(a+b)(b+c)(c+a)` (B) `k a b c(a^2+b^(2)+c^2)` (C) `k(a-b)(b-c)(c-a)` (D) `k(a+b-c)(b+c-a)(c+a-b)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

The value of the determinant |k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1| is k(a+b)(b+c)(c+a) k a b c(a^2+b^(f2)+c^2) k(a-b)(b-c)(c-a) k(a+b-c)(b+c-a)(c+a-b)

Prove that =|1 1 1 a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=(a-b)(b-c)(c-a)

By using properties of determinants , show that : (i) {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) (ii) {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c)

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

Prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

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

Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

CENGAGE-DETERMINANTS-All Questions
  1. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

    Text Solution

    |

  2. Solve by Cramers rule x+y+z=6 x-y+z=2 3x+2y-4z=-5

    Text Solution

    |

  3. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

    Text Solution

    |

  4. Find the value of aa n db if the system of equation a^2x-b y=a^2-ba...

    Text Solution

    |

  5. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

    Text Solution

    |

  6. f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)(xvec0)(f(x))/x ...

    Text Solution

    |

  7. If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x...

    Text Solution

    |

  8. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

    Text Solution

    |

  9. If |a^2+lambda^2a b+clambdac a-blambdaa b-clambdab^2+lambda^2b c+...

    Text Solution

    |

  10. Value of |1+x1 1+x1x1+x1x^2 1+x2 1+x2x1+x2x^2 1+x3 1+x3x1+x3x^2| depen...

    Text Solution

    |

  11. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

    Text Solution

    |

  12. The value of determinant |b c-a^2a c-b^2a b-c^2a c-b^2a b-c^2b c-a^2a ...

    Text Solution

    |

  13. The value of the determinant (a1-b1)^2(a1- ...

    Text Solution

    |

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

    Text Solution

    |

  15. Integrate (sinx)/((sinx-cosx))dx=?

    Text Solution

    |

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

    Text Solution

    |

  17. Let |{:(x,,2,,x),(x^(2),,x,,6),(x,,x,,6):}|=Ax^(4) +Bx^(3)+Cx^(2)+Dx+E...

    Text Solution

    |

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

    Text Solution

    |

  19. The value of the determinant |[sintheta, costheta, sin2theta] , [sin(t...

    Text Solution

    |

  20. Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,...

    Text Solution

    |