Home
Class 12
MATHS
' I ' is the incentre of triangle A B C ...

`' 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`

A

0

B

(a+b+c)BC

C

(a+b+c)AC

D

(a+b+c)AB

Text Solution

Verified by Experts

Let the incentre be at the origin and be
`A(p),B(q) and C(r)`. Then
`IA=p,IB=q and IC=r`
Incentre I is `(ap+bq+cr)/(a+b+c)`, where p=BC,q=AC and r=AB incentre is at the origin. Therefore,
`(ap+bq+cr)/(a+b+c)=0`,
or `ab+bq+cr=0`
`implies aIA+bIB+cIC=0`.
Promotional Banner

Similar Questions

Explore conceptually related problems

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If vec a xxvec b = vec b xxvec c = vec c xxvec a then vec a + vec b + vec c =

If vec a xxvec b = vec b xxvec c = vec c xxvec a then vec a + vec b + vec c =

If vec a xxvec b = vec b xxvec c = vec c xxvec a then vec a + vec b + vec c =

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

If vec a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec a, vec b, vec c are unit vectors such that vec a + vec b + vec c = vec 0 find the value of vec a * vec b + vec b * vec c + vec c * vec avec a * vec b + vec b * vec c + vec c * vec a