Home
Class 12
MATHS
If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , ...

If `abs((a,b,a-b),(b,c,b-c),(2,1,0))=0` , then prove that a,b,c are in GP.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

If (b+c)/a,(c+a)/b,(a+b)/c are in A.P.,prove that 1/a,1/b,1/c are in A.P. given a+b+cne0.

If D=abs((a,b,c),(c,a,b),(b,c,a)) and D'=abs((b+c,c+a,a+b),(a+b,b+c,c+a),(c+a,a+b,b+c)) prove that D'=2D

If (a-c)^2,(c-a)^2,(a-b)^2 are in A.P.,prove that 1/(b-c),1/(c-a),1/(a-b) are in A.P.

If a^2,b^2,c^2 are in A.P. prove that 1/(b+c),1/(c+a),1/(a+b) are in A.P.

If |[a,b,c],[b,a,b],[x,b,c]|=0 then x=____.

If 1/a,1/b,1/c are in A.P. and a+b+cne0_2 prove that (b+c)/a,(c+a)/b,(a+b)/c are in A.P.

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Let f = {(1,3), (2,4), (3,7)} and g = {(3,2), (4,3), (7,1)} determine ...

    Text Solution

    |

  2. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

    Text Solution

    |

  3. If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...

    Text Solution

    |

  4. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

    Text Solution

    |

  5. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

    Text Solution

    |

  6. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

    Text Solution

    |

  7. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

    Text Solution

    |

  8. Prove that d/dxlntan(pi/4+x/2)=secx.

    Text Solution

    |

  9. Determine the point on the curve y = ln x, at which the tangent will b...

    Text Solution

    |

  10. Find the angle of intersection of two curves y =2^x and y=5^x

    Text Solution

    |

  11. If 2y=x(1+(dy)/(dx)), then show that y(2) is a constant.

    Text Solution

    |

  12. Find the solution of the following differential equations: (4x+6y+5)dx...

    Text Solution

    |

  13. int(xe^x)/(1+x^2)dx

    Text Solution

    |

  14. Solve dy/dx-y=e^x.

    Text Solution

    |

  15. Evaluate int(-2)^2abs([x])dx.

    Text Solution

    |

  16. intdx/(sqrtx-root(3)(x))(x=t^6)

    Text Solution

    |

  17. Find the co-ordinates of the foot of the perpendicular from the point ...

    Text Solution

    |

  18. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

    Text Solution

    |

  19. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

    Text Solution

    |

  20. If the magnitude of the difference of two unit vectors is sqrt3 then f...

    Text Solution

    |