IIT JEE , AIEEE Forum - Mathematics , Vectors

karthik_abiram

Q] Let OA=a and OB =b

a vector along one of the bisectors of the angle

AOB is

1]a +b

2]a-b

3]a - b

------ ------

/a/ /b/

4]a+b

---------

/a+b/

Note:OA,OB ,a,b are all in vectors......................i m getting the answer as option [1]

but the answer is given as option [3]

plzz help

kghedriu

see.....this is the proof for the equation of angle bisectors between the lines

r =a+tb and r= a+pc where a,b,c are vectors.....t and p are scalars...

frm the foll fig...

let AL and AM be the given lines such tht a is the position vector of the point A

let P,Q,R be at unit distances frm A and let the midpoints of of PQ and QR be E,F........

.: AE,AF are the bisectors of the angles...

position vec of P,Q,R are

a+b/[b] , a+c/[c] , a-b/[b] where [x] means mod x...

so, position vectors of E,F are:

a+1/2*{ b/[b] + c/[c] } and a + 1/2* { c/[c] - b/[b]}

so, eqn of bisectors are:

r= a+ t{ b/[b]+c/[c]} and r= a+p{c/[c]-b/[b]} where t and p are scalars.......

so, using this, taking a as origin, acc to ur sum, we get the answer as

a/[a] + b/[b] and a/[a]-b/[b]........i.e third option..

so, u got the eqn of both bisectors now!....

hope m clear..

thank u...

Goutham..

aks1