Question

 The vector  bisecting the angle AOB and C being a point on the line AB is  

Solution

Correct option is

 

Taking O as the origin, the position vectors of A and B are  respectively.   

So, the bisector OC of  meets AB at its mid-point C.   

 

ALITER:-  The vector equation of the bisector of ∠AOB is given by   

           

  

The vector equation of line AB is   

        

For the point C to lie on AB, we must have

      

  

   

     

SIMILAR QUESTIONS

Q1

ABCD is a parallelogram with AC and BD as diagonals. Then,   

Q2

If OACB is a parallelogram with 

Q3

If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then   

Q4

Let G be the centroid of âˆ† ABC. If  in terms of , is    

Q5

 

The position vectors of the points ABC are ,

 respectively. These points

Q6

If the points with position vectors  are collinear, then p = 

Q7

If the position vector of a point A is  divides AB in the ratio 2 : 3, then the position vector of B is   

Q8

If  are three non-zero vectors, no two of which are collinear and the vector  is collinear with  is collinear with , then  

Q9

If points  are collinear, then a is equal to 

Q10

If the vector  bisects the angle between the vector  and the vector  then the unit vector in the direction of  is