Home
Class 12
MATHS
Let vec(A)D be the angle bisector of ang...

Let `vec(A)D` be the angle bisector of `angle A" of " Delta ABC ` such that `vec(A)D=alpha vec(A)B+beta vec(A)C,` then

A

`alpha = (|vec(AB)|)/(|vec(AB) + vec(AC)|), beta = (|vec(AC)|)/(|vec(AB) + vec(AC)|)`

B

`alpha =(|vec(AB)| + |vec(AC)|)/(|vec(AB)|), beta =(|vec(AB) + vec(AC)|)/(|vec(AC)|)`

C

`alpha =(|vec(AC)|)/(|vec(AB)+ vec(AC)|), beta =(|vec(AB)|)/(|vec(AB) + vec(AC)|)`

D

`alpha = |(vec(AB))/(vec(AC))|, beta =|(vec(AB))/(vec(AB))|`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

Let vec AD be the angle bisector of /_A of Delta ABC such that vec AD=alphavec AB+betavec AC THEN

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

Let vec(alpha),vec(beta) and vec(gamma be the unit vectors such that vec(alpha) and vec(beta) are mutually perpendicular and vec(gamma) is equally inclined to vec(alpha) and vec(beta) at an angle theta . If vec(gamma)=xvec(alpha)+yvec(beta)+z(vec(alpha)xxvec(beta)) , then which one of the folllowing is incorrect?

Unit vectors vec aa n d vec b are perpendicular, and unit vector vec c is inclined at angle theta to both vec aa n d vec bdot If vec c=alpha vec a+beta vec b+gamma( vec axx vec b), then (a)alpha=beta (b) gamma^2=1-2alpha^2 (c) gamma^2=-cos2theta (d) beta^2=(1+cos2theta)/2

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec(b) + vec(c) = 0 and |vec(a)|=10, |vec(b)|=6 and |vec(c) |=14 . What is the angle between vec(a) and vec(b) ?

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.