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)

Text Solution

Verified by Experts

The correct Answer is:
`AG_(1), BG_(2), CG_(3) and DG_(4)`
Promotional Banner

Topper's Solved these Questions

  • ADDITION OF VECTORS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise - 4 (a) |25 Videos

  • ADDITION OF VECTORS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise - 4 (b) |11 Videos

  • APPLICATION OF DERIVATIVES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise-10(h)|35 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.

If bar(a), bar(b), bar(c ) respresents the vertices A, B, and C respectively of DeltaABC then prove that |(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))| is twice the area of DeltaABC .