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 and vec b are two non- zero vectors such that | vec a + vec b| = |vec a - vec b| , then show that vec a and vec b are perpendicular.

If vector vec a+ vec b bisects the angle between vec a and vec b , then prove that | vec a| = | vec b| .

If vec a and 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].

If vec a and vec b are two unit vectors such that vec a+ vec b and vec a−2 vec b are perpendicular to each other, then the angle between vec a and vec b is

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

If vec a and vec b are orthogonal vectors, prove that (vec a + vec b)^(2) = (vec a - vec b)^(2) .

If vec a and vec b be two unit vectors such that vec a+ vec b is also a unit vector, then find the angle between vec a and vec b

If vec a , vec ba n d vec c are non coplanar vectors and vec axx vec c is perpendicular to vec axx( vec bxx vec c), then the value of [axx( vec bxx vec c)]xx vec c is equal to a. [ vec a vec b vec c] b. 2[ vec a vec b vec c] vec b c. vec0 d. [ vec a vec b vec c] vec a

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .