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

Similar Questions

Explore conceptually related problems

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

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)

(vec b xx vec c) xx (vec c xx vec a ) =

If A, B and C are the vertices of a triangle ABC, then what is the value of vec(AB) + vec(BC) + vec(CA) ?

[vec a + vec b vec b + vec c vec c + vec a] =

' I ' is the incentre of triangle A B C whose corresponding sides are a , b ,c , rspectively. a vec I A+b vec I B+c vec I C is always equal to a. vec0 b. (a+b+c) vec B C c. ( vec a+ vec b+ vec c) vec A C d. (a+b+c) vec A B

Two planes are perpendicular to one another. One of then contains vectors vec a and vec c and other contains vectors vec b and vec d then (vec a xx vec c) . (vec b xx vec d) =

The centroid of the triangle ABC where A= (2,3), B= (8,10) and C= (5,5) is

vec a .[(vec b + vec c) xx (vec a + vec b + vec c)] =