`vec a` and `vec b` are unit vectors making equal angles with `x` -axis at a point `O`. `vec a` is approaching while `vec b` is moving away from point `O`. If `vec a-vec b=2(vec a*vec b)vec c,` find `vec c`

If vec a and vec b are unit vectors find the angle between vec a+vec b and vec a-vec b

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec a,vec b and vec c be any three vectors then show that vec a+(vec b+vec c)=(vec a+vec b)+vec c

if vec a,vec b and vec c are there mutually perpendicular unit vectors and vec a ia a unit vector make equal angles which vec a,vec b and vec c then find the value of |vec a+vec b+vec c+vec d|^(2)

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

If vec a,vec b, and vec c are mutually perpendicular vectors of equal magnitudes,then find the angle between vectors vec a and vec a+vec b+vec c

For any three vectors vec a, vec b, vec c, (vec a-vec b) * (vec b-vec c) xx (vec c-vec a) is equal to

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to