Question

The position vectors of the vertices ABC of a âˆ†ABC are  respectively. The length of the bisector AD of the angle BAC where D is on the line segment BC, is     

Solution

Correct option is

None of these

 

We have,

                 

  

Clearly, point D divides BC in the ratio ABAC i.e. 1 : 3. 

  

  

  

  

SIMILAR QUESTIONS

Q1

If O and O denote respectively the circum-centre and orthocenter of âˆ†ABC, then  

Q2

Consider âˆ†ABC and ∆A1B1C1 in such a way that  and M, N, M1, N1 be the mid-point of AB, BC, A1B1 and B1C1 respectively. Then,  

Q3

Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then  equals

Q4

If A, B, C, D be any four points and E and F be the middle points of AC and BD respectively, then  is equal to

Q5

Given that the vectors  are non-collinear, the values of x and yfor which the vector equality  holds true if  are  

Q6

Let  be three non-zero vectors, no two of which are collinear. If the vector  is collinear with  is collinear with  is equal to 

Q8

 

If the position vector of the three points are ,

 then the three points are 

Q9

Three points with position vectors  will be collinear, if there exist scalars xyz such that   

Q10

 

Consider points ABC and D with position vectors 

 respectively. Then, ABCD is a