Forces `3O vec A ,\ 5O vec B` act along `O A\ a n d\ O B` If their resultant passes through `C` on `AB` , then `C` is a

Forces 3 O vec A , 5 O vec B act along OA and OB. If their resultant passes through C on AB, then

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.

Two forces 4N and 3N act at an angle of 90o.The magnitude of their resultant is (a)4N (b)3N (c)5N (d)7N

The base of the pyramid A O B C is an equilateral triangle O B C with each side equal to 4sqrt(2),O is the origin of reference, A O is perpendicualar to the plane of O B C and | vec A O|=2. Then find the cosine of the angle between the skew straight lines, one passing though A and the midpoint of O Ba n d the other passing through O and the mid point of B Cdot

Five forces vec AB,vec AC,vec AD,vec AE and vec AF act at the vertex of a regular hexagon ABCDEF . Prove that the resultant is 6vec AO, where O is the centre of heaagon.

In a quadrilateral A B C D , bisectors of angles A\ a n d\ B intersect at O such that /_A O B=75^0, then write the value of /_C+\ /_D

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0

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]) .

The diagonals of the parallelogram ABCD intersect at E. If vec a,vec b,vec c and vec a be the position vectors of its vertices with respect to an arbitrary origin O, then show that vec a+vec b+vec c+vec d=4 vec(OE) .