Question

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

Solution

Correct option is

 

Since F is the middle point of BD. Therefore,

        

Similarly, we have  

      

Adding (i) and (ii), we get   

            

  

                                                            [∵ E is the mid-point of AC].

SIMILAR QUESTIONS

Q1

If  are the position vectors of A, B respectively and C is a point on AB produced such that AC = 3 AB, then the position vector of C is 

Q2

Let  be the angle bisector of A of ∆ABC such that  then

Q3

Let D, E, F be the middle points of the sides BC, CA, AB respectively of a triangle ABC. Then,  equals

Q4

If G is the centroid of a triangle ABC, then  equals 

Q5

Let ABC be a triangle having its centroid at G. If S is any point in the plane of the triangle, then 

Q6

If O and O denote respectively the circum-centre and orthocentre of∆ABC, then 

Q7

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

Q8

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,  

Q9

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

Q10

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