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 c |`

If vec a , vec b , vec c are mutually perpendicular unit vectors, find |2 vec a+ vec b+ vec c|dot

vec a , vecb , vec c are three mutually perpendicular unit vectors then |vec a + vec b + vec c| is equal to

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] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

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 ba n d vec c are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is 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

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

Let vec a , vec ba n d vec c be three verctors such that vec a!=0,| vec a|=| vec c|=1,| vec b|=4 and | vec bxx vec c|=sqrt(15)dot If vec b-2 vec c=lambda vec a , then find the value of lambda

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 dot

If vec a , vec b ,a n d vec c are non-zero vectors such that vec a. vec b= vec a. vec c , then find the geometrical relation between the vectors.

If vec a , vec b , and 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| .