Home
Class 11
MATHS
Let bar(a), bar(b), bar(c), bar(d) be th...

Let `bar(a), bar(b), bar(c), bar(d)` be the position vectors of A, B, C and D respectively which are the vertices of a tetrahedron. Then prove that the lines joining the vertices to the centroids of the opposite faces are concurrent. (This point is called the centroid of the tetrahedron)

A

`bar(a)+bar(b)=bar(c)+bar(d)`

B

`bar(a)+bar(b)=bar(c)+bar(d)=bar(0)`

C

`bar(a)+bar(c)=bar(b)+bar(d)`

D

`bar(a)+bar(c)=bar(b)+bar(d)=bar(0)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF VECTORS

    AAKASH SERIES|Exercise EXERCISE - II|77 Videos

  • PROPERTIES OF TRIANGLES

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL II) (Linked Comprehension Type Questions Passage -III:)|3 Videos

  • RATE MEASUREMENT

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE - 1) (LEVEL - 1) (STRAIGHT OBJECTIVE TYPE QUESTION)|43 Videos

Similar Questions

Explore conceptually related problems

If bar(a), bar(b), bar(c) are the position vectors of the vertices A, B, C respectively of DeltaABC then find the vector equation of the median through the vertex A.

If bar(a), bar(b), bar(c) are the position vectors of the vertices A, B, C of the triangle ABC, then the equation of the median from A to BC is

In Delta ABC, if bar(a), bar(b), bar(c) are position vectors of the vertices A, B, and C respectively, then prove that the position vector of the centroid G is (1)/(3) (bar(a) + bar(b) + bar(c))

If bar(a), bar(b), bar(c ) are P.V's of the vertices A,B,C respectively of DeltaABC then find the vector equation of the median through the vertex A.

The position vectors A, B are bar(a), bar(b) respectively. The position vector of C is (5bar(a))/3-bar(b) . Then

The position vectors of A and B are bar(a) and bar(b) respectively. If C is a point on the line bar(AB) such that bar(AC)=5bar(AB) then find the position vector of C.

AAKASH SERIES-PROPERTIES OF VECTORS-PRACTICE EXERCISES
  1. Find the area of the parallelogram whose adjacent sides are bar(a) = 2...

    Text Solution

    |

  2. If the diagonals of a parallelogram are bar(i)+5bar(j)-2bar(k) and -2b...

    Text Solution

    |

  3. Let bar(a), bar(b), bar(c), bar(d) be the position vectors of A, B, C ...

    Text Solution

    |

  4. If bar(a), bar(b) represent bar(AB), bar(BC) respectively of a regular...

    Text Solution

    |

  5. When a right handed rectangular cartesian system oxyz is rotated about...

    Text Solution

    |

  6. The P.V.'s of A, B are bar(a), bar(b) respectively. The P.V. of 'C' is...

    Text Solution

    |

  7. The P.V.'s of A, B are bar(a), bar(b) respectively. The P.V. of 'C' is...

    Text Solution

    |

  8. The vector equation to the line through the point (2, 3, 1) and parall...

    Text Solution

    |

  9. Find the vector equation of the line passing through the points 2bar(i...

    Text Solution

    |

  10. Cartesian equation of the line passing through the points bar(a)=2bar(...

    Text Solution

    |

  11. The cartesian equation of the line passing through the points bar(a)=(...

    Text Solution

    |

  12. Find the vector equation of the line passing through the points bar(i)...

    Text Solution

    |

  13. The vector equation of the plane passing through the point 2bar(i)+2ba...

    Text Solution

    |

  14. The vector equation of the plane passing through the origin and the po...

    Text Solution

    |

  15. If 2bar(i)-bar(j)+bar(k), bar(i)-3bar(j)-5bar(k), 3bar(i)-4bar(j)-4bar...

    Text Solution

    |

  16. The vector equation of the line passing through the point 2bar(i)+bar(...

    Text Solution

    |

  17. If A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-bar(j)+8bar(k)), C(-4bar(i)+4b...

    Text Solution

    |

  18. A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-...

    Text Solution

    |

  19. The point of intersection of the lines bar(r)=bar(a)+t(bar(b)+bar(c)),...

    Text Solution

    |

  20. The point P on the line passing through A(3bar(i)+2bar(j)-3bar(k)) and...

    Text Solution

    |