Prove that the resultant of two forces acting at point O and represented by ` vec O B` and ` vec O C` is given by 2` vec O D` ,where D is the midpoint of BC.

Prove that the resultant of the vectors represented by the sides vec(AB) and vec(AC) of a triangle ABC is 2 vec(AD) , where D is the mid - point of [BC].

Vectors drawn the origin O to the points A,B and C are respectively vec a,vec b and vec 4a-3vec b. find vec AC and vec BC

Two forces vec A B and vec A D are acting at vertex A of a quadrilateral ABCD and two forces vec C B and vec C D at C prove that their resultant is given by 4 vec E F , where E and F are the midpoints of AC and BD, respectively.

ABCDE is a pentagon.prove that the resultant of force vec AB,vec AE,vec BC,vec DC,vec ED and vec AC is 3vec AC

Vectors drawn form the origin O to the points A , B and C are respectively veca, b and 4veca -vec(b) Find vec(AC) and vec(BC)

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 E is the intersection point of diagonals of parallelogram ABCD and vec( OA) + vec (OB) + vec (OC) + vec (OD) = xvec (OE) where O is origin then x=

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.

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.

If vec a,vec b,vec c are position vectors o the point A,B, and C respectively,write the value of vec AB+vec BC+vec AC