Home
Class 12
MATHS
If the centroid of the tetrahedron O-ABC...

If the centroid of the tetrahedron O-ABC, where `A-=(alpha,5,6), B-=(1,beta,4)` and `C-=(3,2,gamma)` is `G(1,-1,2)`, then: `alpha^(2) + beta^(2) + gamma^(2)=`

A

`alpha^(2) + beta^(2)`

B

`beta^(2) + gamma^(2)`

C

`gamma^(2)+alpha^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise PREVIOUS YEAR MHT-CET EXAM QUESTIONS|3 Videos

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP- CHAPTERS 6,7,8|16 Videos

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP- CHAPTERS 6,7,22|1 Videos

  • PAIR OF STRAIGHT LINES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|19 Videos

  • THREE DIMENSIONAL GEOMETRY

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|39 Videos

Similar Questions

Explore conceptually related problems

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 the centroid of a triangle with vertices (alpha, 1, 3), (-2, beta, -5) and (4, 7, gamma) is the origin then alpha beta gamma is equal to …..........

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 .

A variable plane is at a constant distance 3p from the origin and meets the coordinates axes in A,B and C if the centroid of triangle ABC is (alpha,beta,gamma ) then show that alpha^(-2)+beta^(-2)+gamma^(-2)=p^(-2)

If the centroid of triangles formed by the vertices (1, 2, 3), (2, 1, 0) and (3, 1, 4) is (alpha, beta, gamma) then the value of [alpha]+[beta]+[gamma], where [ ] represents the greatest integer function, is _______.

If alpha+beta+gamma=6,alpha^(2)+beta^(2)+gamma^(2)=14 and alpha^(3)+beta^(3)+gamma^(3)=36, then alpha^(4)+beta^(4)+gamma^(4)=

For alpha, beta, gamma in R , let A=[(alpha^(2),6,8),(3,beta^(2),9),(4,5,gamma^(2))] and B=[(2alpha,3,5),(2,2beta,6),(1,4,2gamma-3)]

If [(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] is orthogonal, then find the value of 2alpha^(2)+6beta^(2)+3gamma^(2).

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

Q.show that det [[- alpha (2), alpha beta, gamma alphaalpha beta, -beta ^ (2), beta gammagamma alpha, beta gamma, -gamma ^ (2)]] = 4 alpha ^ (2) beta ^ (2) gamma ^ (2)

MARVEL PUBLICATION-PLANE IN SPACE -PART B: MASTERING THE BEST ON LINE AND PLANE IN SPACE
  1. The perpendicular distance of a corner of uni cube from a diagonal not...

    Text Solution

    |

  2. A line makes an angle alpha, beta, gamma, delta with the four diagonal...

    Text Solution

    |

  3. If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,...

    Text Solution

    |

  4. The shortest distance between the lines x+a=2y=-12z and x=y+2a=6z-6a i...

    Text Solution

    |

  5. The direction Cosines of two lines at right angles are l(1),m(1),n(1)a...

    Text Solution

    |

  6. Two system of rectangular axes have the same origin. If a plane cuts t...

    Text Solution

    |

  7. If h, m1, n1 and l2, m2, n2 are D.C.s of the two lines inclined to eac...

    Text Solution

    |

  8. Let vectors bara, barb, barc and bard be such that (baraxxbarb)xx(ba...

    Text Solution

    |

  9. A non zero vector veca is parallel to the kine of intersection of the ...

    Text Solution

    |

  10. Value of k such that the line (x-4)/1 = (y-2)/1 =(z-k)/2 lies in th...

    Text Solution

    |

  11. IF lines (x-1)/(2) =(y+1)/(3) =(z-1)/(4) and x-3 =(y-k) /(2) = z ...

    Text Solution

    |

  12. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

    Text Solution

    |

  13. If the straight lines (x-1)/k = (y-2)/2 =(z-3)/3 and (x-2)/3 = (y-3)...

    Text Solution

    |

  14. A variable plane at distance of 1 unit from the origin cuts the coordi...

    Text Solution

    |

  15. If the lines x=ay +b, z=cy+d and x=a'y + b', z=c'y + d' are perpendi...

    Text Solution

    |

  16. The angle between the lines 2x=3y=-z and 6x=-y=-4z is

    Text Solution

    |

  17. A plane which passes through the point (3,2,0), and the line (x-3)/1 =...

    Text Solution

    |

  18. Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=...

    Text Solution

    |

  19. The line passing through the points (5,1,a) and (3,b,1) crosses the y...

    Text Solution

    |

  20. Let the line (x-2)/3 = (y-1)/-5 =(z+2)/2 lie in the plane x+3y - alpha...

    Text Solution

    |