Home
Class 12
MATHS
The determinant |[y^2,-x y, x^2],[a, b, ...

The determinant `|[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']|` is equal to a.`|[b x+a y, c x+b y],[ b^(prime)x+a ' y, c^(prime)x+b ' y]|` b. `|[a x+b y, b x+c y],[ a^(prime)x+b ' y, b ' x+c ' y]|` c. `|[b x+c y, a x+b y],[ b^(prime)x+c ' y, a^(prime)x+b ' y]|` d. `|[a x+b y, b x+c y],[ a^(prime)x+b ' y, b^(prime)x+c ' y]|`

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 x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a y]|=x y z|[a, b, c],[c ,a ,b],[b ,c ,a]|

Factorize: a x+b x+a y+b y +a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+a c + a x-a y+b x-b y

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 z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Find the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d ' are perpendicular.

If a, b, c are in GP and a, x, b, y are in AP Then prove that, a/x + c/y = 2

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is a. 3abc b. 6abc c. abc d. 4abc

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

If X= { a, b, c, d } and Y = { f, b, d, g} , find X – Y

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b...

    Text Solution

    |

  2. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

    Text Solution

    |

  3. The determinant |[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']| is equal ...

    Text Solution

    |

  4. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

    Text Solution

    |

  5. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

    Text Solution

    |

  6. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

    Text Solution

    |

  7. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

    Text Solution

    |

  8. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

    Text Solution

    |

  9. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of de...

    Text Solution

    |

  10. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

    Text Solution

    |

  11. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

    Text Solution

    |

  12. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

    Text Solution

    |

  13. Which of the following has/have value equal to zero? |[8, 2, 7],[ 12, ...

    Text Solution

    |

  14. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  15. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

    Text Solution

    |

  16. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

    Text Solution

    |

  17. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

    Text Solution

    |

  18. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

    Text Solution

    |

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

    Text Solution

    |

  20. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

    Text Solution

    |