Let ` vec a , vec ba n d vec c` be pairwise mutually perpendicular vectors, such that `| vec a|=1,| vec b|=2,| vec c|=2.` Then find the length of ` vec a+ vec b+ vec cdot`

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, vec c are any three mutually perpendicular vectors of equal magnitude a, then |vec a+ vec b+ vec c| is equal to

Let vec a , vec ba n d vec c be three units vectors such that 2 vec a+4 vec b+5 vec c=0. Then which of the following statement is true? a. vec a is parallel to vec b b. vec a is perpendicular to vec b c. vec a is neither parallel nor perpendicular to vec b d. none of these

If vec a , vec b ,a n d vec c are mutually perpendicular vectors and vec a=alpha( vec axx vec b)+beta( vec bxx vec c)+gamma( vec cxx vec a)a n d[ vec a vec b vec c]=1, then find the value of alpha+beta+gammadot

If vec a , vec ba n d vec c are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is a. vec a+ vec b+ vec c b. vec a/(| vec a|)+ vec b/(| vec b|)+ vec c/(| vec c|) c. vec a/(| vec a|^2)+ vec b/(| vec b|^2)+ vec c/(| vec c|^2) d. | vec a| vec a-| vec b| vec b+| vec c| vec c

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 ,a n d vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a ,a n d vec bdot

If vec a , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec adot vec x=1, vec bdot vec x=3/2,| vec x|=2. Then find the angel between cc and xxdot

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .