if ` vec (AO)` + ` vec (O B)` = ` vec (B O)` + ` vec (O C)` ,than prove that `B` is the midpoint of `AC`.

If vec A O+ vec O B= vec B O+ vec O C , then A ,B and C are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these

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.

If vec(AO)+vec(OB)=vec(BO)+vec(OC) , show that the points A, B and C are collinear.

If vec (a) + vec(b) + vec (c ) = vec(0) and |vec(a)| = 6 , |vec (b)| = 4 and |vec(c )| = 3 find the cosine of the angle between the vectors vec(b) and vec(c )

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

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.

If O A B C is a tetrahedron where O is the origin and A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

If 2vec(AC)=3vec(CB) , then prove that 2vec(OA)+3vec(OB)=5vec(OC) where O is the origin.

Three vectors vec(a),vec(b),vec (c ) are such that vec(a) + vec(b) + vec(c ) = vec(0) , if |vec(a)| = 1 |vec(b)| = 4 and |vec(c )|= 2 , then find the value of mu = (vec(a).vec(b) +vec(b).vec(c ) + vec(c ).vec(a))