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.) `1` (d.) 3

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 a. 0 b. 1 c. -sqrt(3) d. sqrt(3)

Let vec a , vec b ,a n d 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]^2dot

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

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

If vec a, vec b, vec c are three given vectors show that [ vec a + vecb + vec c , vecb + vec c , vec a + vec b + vec c ]=0.

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 non-coplanar vectors, prove that vectors 3vec a-7 vec b-4 vec c ,3 vec a -2 vec b+ vec c and vec a + vec b +2 vec c are coplanar.

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 .

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 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