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

If | vec AO + vec OB | = | vec BO + vec OC |, then A, B, C form

If vec AO+vec OB=vec BO+vec OC, prove that A,B,C are collinear points.

If O A B C is a tetrahedron where O is the orogin anf 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 , 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 vec AO+vec OB=vec BO+vec OC, then A,quad B nad C are (where O is the origin) a.coplanar b. collinear c.non-collinear d.none of these

If three vectors vec A, vec B and vec C are such that vec A .vec B =vec A .vec C , vec A xx vec B = vec A xx vec C , vec A!= vec 0 then prove that vec B =vec C .

If vec c is perpendicular to both vec a and vec b, then prove that it is perpendicular to both vec a+vec b and vec a-vec b .

If vec c is perpendicular to both vec a and vec b, then prove that it is perpendicular to both vec a+vec b and vec a-vec b

For two vectors vec(A) and vec(B) if vec(A) + vec(B) = vec(C) and A +B = C , then prove that vec(A) and vec(B) are parallel to each other.

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