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.

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

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.

If ABCD is quadrilateral and E and F are the mid-points of AC and BD respectively, prove that vec AB+vec AD+vec CB+vec CD=4vec EF

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

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

ABCD is a parallelogram with AC and BD as diagonals. Then, A vec C - B vec D =

If vec a,vec b,vec c and vec d are distinct vectors such that vec a xxvec c=vec b xxvec d and vec a xxvec b=vec c xxvec d prove that (vec a-vec d)vec b-vec c!=0

Give vec A + vec B+ vec C + vec D =0 , which of the following statements are correct ? (a) vec A, vec B ,vec C abd vec C must each be a null vector. (b) The magnitude of ( vec A + vec C) equals the magnitude of ( vec B + vec D0 . ltBrgt (c ) The magnitude of vec A can never be greater than the sum of the magnitude of vec B , vec C and vec D . ( d) vec B + vec C must lie in the plance of vec A + vec D. if vec A and vec D are not colliner and in the line of vec A and vec D , if they are collinear.

Suppose you two forces vec Fand vec F . How would you combine then in order to have resultant force of magnitudes (a) zero (b) 2 vec F and (c 0 vec F .

For any four vectors,vec a,vec b,vec c and vec d prove that vec d*(vec a xx(vec b xx(vec c xxvec d)))=(vec b*vec d)[vec avec cvec d]