Home
Class 12
MATHS
Let a,b,c be in A.P and x,y,z be in G.P....

Let a,b,c be in A.P and x,y,z be in G.P.. Then the points `(a,x),(b,y)` and `(c,z)` will be collinear if

A

A. `x^2=y`

B

B. `x=y=z`

C

C. `y^2=z`

D

D. `x=z^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that a,b,c are in A.P.
`rArra-b=b-c`
Now, `(a,x),(b,y)and (c,z)` are collinear.
`rArr(x-y)/(a-b)=(y-z)/(b-c)`
`rArr (x-y)/(y-z)=(a-b)/(b-c)=1`
`rArrx-y=y-z`
So, x,y,z are in A.P.
Thus x,y,z are in A.P and also in G.P.
`therefore x=y=z`.
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Multiple correct|13 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Linked|10 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^(c-a).z^(a-b) = 1 .

If a,b,c are in A.P and x,y,z are in G.P prove that (b-c) logx+(c-a) log y+(a-b) log z=0

If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (d-a) are in G.P.

If a,b,c are in A.P and x,y,z are in G.P then prove that a^((b-c)log_(a)^(x))xxb^((c-a)log_(b)^(y))xxc^((a-b)log_(c )^(z))=1

Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3w h e na ,x ,y ,z ,b are in H.P. Then (i) G.M. of a and b is 3 (ii) One possible value of a+2b is 11 (iii) A.M. of a and b is 6 (iv) Greatest value of a-b is 8

If a, b, c are in AP, a, x, b are in GP , where as b, y and c also in GP. Then prove that x^2, b^2, y^2 are in AP.

If a ,b ,c ,d ,e , and f are in G.P. then the value of |((a^2),(d^2),x),((b^2),(e^2),y),((c^2),(f^2),z)| depends on (A) x and y (B) x and z (C) y and z (D) independent of x ,y ,and z

If x ,y ,a n dz are distinct prime numbers, then (a). x , y , a n dz may be in A.P. but not in G.P. (b) x , y , a n dz may be in G.P. but not in A.P. (c). x , y , a n dz can neither be in A.P. nor in G.P. (d).none of these

Let A(z_1),B(z_2) and C(z_3) be the three points in Argands plane The point A B and C are collinear if

If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c respectively, prove that, (a)/(x) + (c )/(y) = 2

CENGAGE PUBLICATION-COORDINATE SYSYEM -Exercises
  1. The vertices of a parallelogram A B C D are A(3,1),B(13 ,6),C(13 ,21),...

    Text Solution

    |

  2. Point A and B are in the first quadrant,point O is the origin. If the ...

    Text Solution

    |

  3. Let a,b,c be in A.P and x,y,z be in G.P.. Then the points (a,x),(b,y) ...

    Text Solution

    |

  4. If sum(i=1)^4(x1^2+y 1^2)lt=2x1x3+2x2x4+2y2y3+2y1y4, the points (x1, y...

    Text Solution

    |

  5. The vertices A and D of square A B C D lie on the positive sides of x-...

    Text Solution

    |

  6. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

    Text Solution

    |

  7. The locus of the moving point whose coordinates are given by (e^t-e^(-...

    Text Solution

    |

  8. The locus of a point reprersented by x=a/2((t+1)/t),y=a/2((t-1)/t) , w...

    Text Solution

    |

  9. Vertices of a variable triangle are A(3,4),B(5costheta, 5sintheta) and...

    Text Solution

    |

  10. Vertices of a variable triangle are A(3,4),B(5costheta, 5sintheta) and...

    Text Solution

    |

  11. From a point, P perpendicular PM and PN are drawn to x and y axis, res...

    Text Solution

    |

  12. The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) ...

    Text Solution

    |

  13. If the roots of the equation (x(1)^(2)-a^2)m^2-2x1y1m+y(1)^(2)+b^2=0...

    Text Solution

    |

  14. Through point P(-1,4), two perpendicular lines are drawn which interse...

    Text Solution

    |

  15. The number of integral points (x,y) (i.e, x and y both are integers) w...

    Text Solution

    |

  16. The foot of the perpendicular on the line 3x+y=lambda drawn from the o...

    Text Solution

    |

  17. The image of P(a,b) on the line y=-x is Q and the image of Q on the li...

    Text Solution

    |

  18. If the equation of the locus of a point equidistant from the points (a...

    Text Solution

    |

  19. Consider three lines as follows. L1:5x-y+4=0 L2:3x-y+5=0 L3: x+y+8=0...

    Text Solution

    |

  20. Consider a point A(m,n) , where m and n are positve intergers. B is th...

    Text Solution

    |