`A B C D` is quadrilateral such that ` vec A B= vec b , vec A D= vec d , vec A C=m vec b+p vec ddot` Show that he area of the quadrilateral `A B C Di s1/2|m+p|| vec bxx vec d|dot`

The position vectors of the vertices of a quadrilateral with A as origin are B(vec b),D(vec d) and C(lvec b+mvec d) Prove that the area of the quadrialateral is (1)/(2)(l+m)|vec b xxvec d|

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

If vec a xxvec b = vec c xxvec d and vec a xxvec c = vec b xxvec d then show that vec a-vec d is parallel to vec b-vec c

Prove that [vec a,vec b,vec c+vec d]=[vec a,vec b,vec c]+[vec a,vec b,vec d]

Given four vectors vec a, vec b, vec c, vec d such that vec a + vec b + vec c = alphavec d, vec b + vec c + vec d = betavec a and that vec a, vec a, vec b, vec c are non-coplanar, then the sum vec a + vec b + vec c + vec d is

If vec a xxvec b=vec c xxvec d and vec a xxvec c=vec b xxvec d then show that vec a-vec d is parallel to vec b-vec c where a!=d and b!=c

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If vec a, vec b, vec c are three non-coplanar vectors such that vec a + vec b + vec c = alphavec d and vec b + vec c + vec d = betavec a then vec a + vec b + vec c + vec d is equal to

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

If vec a xxvec b=vec c xxvec d and vec a xxvec c=vec b xxvec d show that vec a-vec d is parallel to vec b-vec c, where vec a!=vec d and vec b!=vec c