In a triangle OAC, if `B` is the mid point of side AC and ` vec O A= vec a ,\ vec O B= vec b ,\ ` then what is ` vec O C ?`

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

Statement 1: In "Delta"A B C , vec A B+ vec A B+ vec C A=0 Statement 2: If vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b

if vec Ao + vec O B = vec B O + vec O C ,than prove that B is the midpoint of AC.

A B C D is a quadrilateral and E and the point intersection of the lines joining the middle points of opposite side. Show that the resultant of vec O A , vec O B , vec O Ca n d vec O D is equal to 4 vec O E , where O is any point.

Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 Statement 2: If vec (O A)= vec a , vec (O B)= vec b ,t h e n \ vec (A B)= vec a+ vec b

Let O be the centre of a regular hexagon A B C D E F . Find the sum of the vectors vec O A , vec O B , vec O C , vec O D , vec O Ea n d vec O F .

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that vec O Pdot vec O Q+ vec O Rdot vec O S= vec O Rdot vec O P+ vec O Qdot vec O S= vec O Q . vec O R+ vec O Pdot vec O S Then the triangle PQ has S as its: circumcentre (b) orthocentre (c) incentre (d) centroid

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.