If ` vec a ,\ vec b ,\ vec c` be the vectors represented by the sides of a triangle, taken in order, then prove that ` vec a+ vec b+ vec c= vec0dot`

If vec a ,\ vec b ,\ vec c\ represent the sides of a triangle taken in order, then write the value of vec a+ vec b+ vec c

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

If G is the centroid of a triangle A B C , prove that vec G A+ vec G B+ vec G C= vec0dot

If G is the centroid of a triangle A B C , prove that vec G A+ vec G B+ vec G C= vec0dot

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

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

If vec a ,\ vec b ,\ vec c are three vectors such that vec adot vec b= vec adot vec c then show that vec a=0\ or ,\ vec b=c\ or\ vec a_|_( vec b- vec c)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

If vec a,vec b,vec c are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4, (vec a+vec b)+(vec bxx vec c)+(vec b+vec c).(vec c xx vec a) + (vec c +vec a).(vec axx vec b) is equal to

If vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c= vec0, then write the value of vec a . vec b+ vec b . vec c+ vec c . vec a