If `A B C D` is a rhombus whose diagonals cut at the origin `O ,` then proved that ` vec O A+ vec O B+ vec O C+ vec O D` =0

Let A B C D be a parallelogram whose diagonals intersect at P and let O be the origin. Then prove that vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot

Let A B C D be a p[arallelogram whose diagonals intersect at P and let O be the origin. Then prove that vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot

A , B , Ca n dD are any four points in the space, then prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (area of A B C ).

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

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

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Let PQRS be a parallelogram whose diagonals PR and QS intersect at O'. If O is the origin, then (vec(OP)+vec(OQ)+vec(OR)+vec(OS)) is equal to -

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 mutually orthogonal unit vectors, then the triple product [ vec a+ vec b+ vec c vec a+ vec b vec b+ vec c] equals: (a.) 0 (b.) 1 or -1 (c.) 6 (d.) 3

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot