The position vectors of the vertices of a quadrilateral with `A` as origin are `B( vec b),D( vec d)a n dC(l vec b+m vec d)dot` Prove that the area of the quadrialateral is `1/2(l+m)| vec bxx vec d|dot`

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

If vec a , vec b , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot

A B C D is a quadrilateral. Find the sum the vectors vec B A , vec B C , and vec D A .

A B C D is a quadrilateral. Find the sum the vectors vec B A , vec B C , and vec D A .

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vecd dot vec a= vecd dot vec b= vec d dot vec ca n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

If vec a\ a n d\ vec b are vectors of equal magnitude, write the value of ( vec a+ vec b)dot( vec a- vec b)dot

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c

If vec aa n d vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b]dot

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot