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

The correct Answer is:
A
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

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

The position vectors of A, B,C and D are vec a , vec b , vec 2a+ vec 3b and vec a - vec 2b respectively. Show that vec (DB)=3 vec b -vec a and vec (AC) =vec a + vec 3b

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)' =

Statement 1: In "Delta"A B C , vec A B+ vec A B+ vec C A=0 Statement 2: If vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b

(vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )) . If vec(a)*vec( c ) ……………

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

If the lines vec r = vec a + lambda (vec b xx vec c) and vec r = vec b + mu (vec c xx vec a) are intersect then ...............

Prove that [vec(a)+vec(b), vec(b)+vec( c ), vec( c )+vec(a)]=2[vec(a),vec(b),vec( c )] .