If `vec a , vec b , and vec c` are three mutually orthogonal unit vectors, then the triple product`[ vec a+ vec b+ vec c vec a+ vec b vec b+ vec c]` equals: (a.) `0` (b.) `1 or -1` (c.) `6` (d.) 3

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

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

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

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

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.

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

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .

If vec a , vec ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]