Home
Class 12
MATHS
If G is the centroid of Delta ABC and G'...

If G is the centroid of `Delta ABC and G' ` is the centroid of `Delta A' B' C' " then " vec(A A)' + vec(B B)' + vec(C C)' = `

Text Solution

Verified by Experts

Here,
G is centroid of `DeltaABC` and G' is centroid of `DeltaA'B'C'`, shown as in figure.

Clearly, `A A'=AG+G G'+G'A'` (polygon law)
`B B'=BG+G G'+G'B'`
`C C'=CG+CG'+G'C'`
On adding these
`A A'+B B'+C C'=3G G'+(AG+BG+CG)+(G'A'+G'B'+G'C')`
`=3G G'+(AG+2DG)+(G'A'+2G'D')`
(usingg AD and A'D' as the medians of `DeltaABC` and `DeltaA'B'C'`, respectively).
`=3G G'+(AG+GA)+G'A'+A'G'`
`=3G G'+O+O`
`therefore A A'+B B'+C C'=3G G'`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

If A, B, C are vertices of a triangle whose position vectors are vec a, vec b and vec c respectively and G is the centroid of Delta ABC, " then " vec(GA) + vec(GB) + vec(GC), is

D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC and G is the centroid of the triangle, then vec(GD) + vec(GE) + vec(GF) =

If G denotes the centroid of Delta ABC, then write the value o vec GA+vec GB+vec GC

If G is the centroid of a triangle ABC, prove that vec GA+vec GB+vec GC=vec 0

Prove that GvecA+GvecB+GvecC=vec0 , if G is the centroid of Delta ABC.

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

If S is the cirucmcentre, G the centroid, O the orthocentre of a triangle ABC, then vec(SA) + vec(SB) + vec(SC) is:

Let G be the centroid of Delta ABC , If vec(AB) = vec a , vec(AC) = vec b, then the vec(AG), in terms of vec a and vec b, is

If O is the circumcentre,G is the centroid and O' is orthocentre or triangle ABC then prove that: vec OA+vec OB+vec OC=vec OO