Home
Class 12
MATHS
If a , b ,c are all different and |[a,...

If `a , b ,c` are all different and `|[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|=0,` show that `a b c(a b+b c+c a)=a+b+c`

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 all distinct and |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 , show that abc(ab+bc+ca)=a+b+c.

If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0 . Show that either a+b+c=0 or a=b=c

Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)dot

If a^(1/3)+b^(1/3)+c^(1/3)=0 show that (a+b+c)^(3)=27 abc

If a,b and c are real numbers, and Delta ={:|( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) |:}=0 Show that either a+b+c=0 "or" a= b= c .

If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.

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

If a/b = b/c = c/d , then show that (a - b)^(3) : (b - c)^(3) = a : d .

Show that |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3 .

If 2a = 3b = 4c , then a : b : c will be

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

    Text Solution

    |

  2. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

    Text Solution

    |

  3. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

    Text Solution

    |

  4. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

    Text Solution

    |

  5. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

    Text Solution

    |

  6. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(...

    Text Solution

    |

  7. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

    Text Solution

    |

  8. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

    Text Solution

    |

  9. 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)...

    Text Solution

    |

  10. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

    Text Solution

    |

  11. Using the properties of determinants, prove that following |(a-b-c,2a,...

    Text Solution

    |

  12. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[log a...

    Text Solution

    |

  13. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

    Text Solution

    |

  14. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

    Text Solution

    |

  15. The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, co...

    Text Solution

    |

  16. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

    Text Solution

    |

  17. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

    Text Solution

    |

  18. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

    Text Solution

    |

  19. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

    Text Solution

    |

  20. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

    Text Solution

    |