## Question

### Solution

Correct option is

Since F is the middle point of BD. Therefore,

Similarly, we have

Adding (i) and (ii), we get

[âˆµ 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 âˆ†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 ofâˆ†ABC, then

Q7

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

Q8

Consider âˆ†ABC and âˆ†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