" 8."quad " If "|vec a|=|vec b|=|vec a+vec b|=1," then prove that "|vec a-vec b|=sqrt(3)

if | vec a | = | vec b | = | vec a + vec b | = 1 then | vec a-vec b |

If |quad vec a|=1 , |quad vec b|=1 and |quad vec a+ vec b|=1 , prove that | vec a- vec b|= sqrt 3 .

If |vec a|=8, |vec b|=3 and |vec axx vec b|=12 , then the value of vec a . vec b is

If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a - vec b) * (3 vec a + vec b) .

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

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

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

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

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|

Find |vec a| and |vec b|, if (vec a+vec b)(vec a-vec b)=8 and |vec a|=8|vec b|