C is the midpoint of the line segment `bar(AB)` and O is any point outside AB, show that `vec(OA)+vec(OB)=2vec(OC)`.

ABCD is a quadrilateral and E is the point of intersection of the lines joining the mid-points of opposite sides. If O be any point in the plane, then show that vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OE) .

Let D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB) of the triangle ABC. Prove that vec(AD)+vec(BE)+vec(CF)=vec(0) .

If C is the midpoint of AB and P is any point outside AB, then which one of the following is correct ?

D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB) respectively of the triangle ABC. If P is any point in the plane of the triangle, show that vec(PA)+vec(PB)+vec(PC)=vec(PD)+vec(PE)+vec(PF) .

ABCD is a quadrilateral and E is the point of intersection of the lines joining the middle points of opposite side. Show that the resultant of vec (OA) , vec(OB) , vec(OC) and vec(OD) = 4 vec(OE) , where O is any point.

A B C D is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx is equal to a. 3 b. 9 c. 7 d. 4

If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the position vectors of the points A and B respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vectors of the points of trisection of the line-segment bar(AB) .

Let C be the midpoint of the line-segment joining the points A and B , if vec(a) " and " vec(c) are the position vectors of the points A and C respetively, then the position vector of the vector of the point B will be -

The diagonals of the parallelogram ABCD intersect at E. If vec(a), vec(b), vec(c) " and " vec(d) be the position vectors of its vertices with respect to an arbitary origin O, then show that vec(a)+vec(b)+vec(c)+vec(d)=4vec(OE) .

In the DeltaOAB,M is the mid-point of AB,C is a point on OM, such that 2OC=CM. X is a point on the side OB such that OX=2XB. The line XC is produced to meet OA in Y. then, (OY)/(YA) is equal to