Home
Class 11
MATHS
If the origin is the centroid of a trian...

If the origin is the centroid of a triangle ABC having vertices `A(a ,1,3),\ B(-2, b ,-5)a n d\ C(4,7, c)` , find the values of `a , b , cdot`

Text Solution

Verified by Experts

Given that origin is the centroid of the `DeltaABC` i.e. G (0,0,0)
`0= (a-2+4)/3 Rightarrowa=-2`
` 0= (1+b+7)/3Rightarrowb=-8`
`0=(3-5+c)/3Rightarrow c = +2`
a=-2, b=-8 and c=2
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Long Answer type Questions|4 Videos
  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Objective type Questions|13 Videos
  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos
  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR|Exercise FILLERS|4 Videos

Similar Questions

Explore conceptually related problems

If the origin is the centroid of the triangle with vertices P(2a,2,6),Q(-4,3b,-10) abnd R(8,14,2c) ,find the values of a and b .

If the origin is the centroid of the triangle whose vertices are A (2,p,-3), B(q,-2,5) and C(-5,1,r), then find the values of p,q and r.

13.If the origin is the centroid of the triangle PQR with vertices P(2a,2,6) , Q(-4,3b,-10) and R(8,14,2c) then find the values of a,b and c.

If the origin is the centroid of the triangle PQR with vertices P(2a,2,6)Q(-4,3b,-10) and R(8,14,2c) then find the values of a,b and c.

If origin is the centroid of /_\ABC with the vertices A(alpha, 1,3),B(-2,beta, -5) and C(4,7,gamma) find the value of alpha, beta,gamma

If origin is the centroid of the triangle with vertices P(3a, 3, 6), Q (-4, 2b, -8) and R(8, 12, 2c), then the value of a, b, and c are

lf origin is centroid of triangle with vertices (a, 1 , 3), (- 2, b, -5) and (4, 7, c), then (a, b, c) equiv

The origin is the centroid of /_\ABC with the vertices A(alpha, 1, 3),B(-2, beta, -5) and C(4,7,gamma) find the values of alpha, beta, gamma .

If G(a,2,-1) is the centroid of the triangle with vertices P(1,3,2),Q(3,b,-4) and R(5,1,c), then find the values of a,b and c.

If the centroid of Delta ABC having vertices A(a, b), B(b, c) and C(c, a) is the origin, then find the value of (a+b+c).

NCERT EXEMPLAR-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-Fillers
  1. If the origin is the centroid of a triangle ABC having vertices A(a ,1...

    Text Solution

    |

  2. The three axes OX, OY and OZ determine ………….

    Text Solution

    |

  3. The three planes, determine a rectangular parallelopiped which has ………...

    Text Solution

    |

  4. The coordiantes of a point are the perpendicular distance from the ….....

    Text Solution

    |

  5. The Three coordiantes planes divide the space into ……. Parts.

    Text Solution

    |

  6. If a point P lies in YZ- plane , the n the coordinates of a point on Y...

    Text Solution

    |

  7. The equation of YZ- plane is ………

    Text Solution

    |

  8. If the point P lies on Z - axis , then coordinates of p are of the for...

    Text Solution

    |

  9. The equation of Z - axis , are…………..

    Text Solution

    |

  10. A line is parallel to XY- plane if all the points on the line have equ...

    Text Solution

    |

  11. A line is parallel to X-axis,if all the points on the line have equal…...

    Text Solution

    |

  12. 45x=a represent a plane parallel to ………..

    Text Solution

    |

  13. The plane parallel to YZ- plane is perpendicular to ………….

    Text Solution

    |

  14. The length of the longest piece of a string that can be stetched strai...

    Text Solution

    |

  15. If the distance between the points P(a ,2,1)a n d\ Q(1,-1,1) is 5 unit...

    Text Solution

    |

  16. The coordinates of the mid points of sides AB, BC and CA of A B C are...

    Text Solution

    |

  17. Match each item given under the column I to its correct answer given u...

    Text Solution

    |