If `vec a`,`vec b`,`vec c ` are mutually perpendicular unit vectors , then find the value of `|quad 2 vec a+ vec b+ vec c|`.

If vec a, vec b ,vec c are mutually perpendicular vectors of equal magnitudes, show that the vector vec a+ vec b + vec c is equally inclined to vec a, vec b and vec c .

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 three non-coplanar vectors, then find the value of ( vec adot( vec bxx vec c))/( vec b dot( vec cxx vec a))+( vec b dot( vec cxx vec a))/( vec c dot( vec axx vec b))+( vec c dot( vec bxx vec a))/( vec a dot( vec bxx vec c))dot

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

If vec a,vec b,vec c are unit vectors such that vec a+vec b+ vec c= vec 0 , then the value of vec a *vec b +vec b* vec c+ vec c*vec a is equal to

If vec aa n d vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b]dot

If vec a , vec b and vec c are non-coplanar (independent) vectors, prove that the vectors vec a- 2 vec b+ 3 vec c , -2 vec a + 3 vec b- 4 vec c and vec a -vec b+ 2 vec c are also linearly independent.

If vec a , vec b , vec c are unit vectors such that vec adot vec b=0= vec adot vec c and the angle between vec ba n d vec c is pi//3 , then the value of | vec axx vec b- vec axx vec c| is 1//2 b. 1 c. 2 d. none of these

If vectors vec a and vec b , are such that |vec a| =3,|vec b| =2/3 and vec a xx vec b is a unit vector, then find the angle between vec a and vec b .

If vec a , vec b are any two vectors, then give the geometrical interpretation of relation | vec a+ vec b|=| vec a- vec b|