If ` vec a ,\ vec b ,\ ` are two vectors such that `| vec a+ vec b|=| vec a|,` then prove that `2 vec a+ vec b` is perpendicular to ` vec bdot`

If vec a , vec b are two vectors such that | vec a+ vec b|=| vec b|, then prove that vec a+2 vec b is perpendicular to vec a .

If vec a ,\ vec b are two vectors such that | vec a+ vec b|\ =| vec b|, then prove that vec a+2 vec b is perpendicular to vec adot

If vec(a) and vec(b) are two vector such that |vec(a) +vec(b)| =|vec(a)| , then show that vector |2a +b| is perpendicular to vec(b) .

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

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

If vec a\ a n d\ vec b are two vectors such that | vec a|=| vec axx vec b|, write the angle between vec a\ a n d\ vec bdot

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 and vec b are two vectors such that | vec a|=2, |vecb|=3 and ( vec a . vec b )=4 then \ f i n d |( vec a - vec b )|

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot

If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b+ vec c= vec0 find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot'