Evaluate :
`[[vec a,vec a,vec a]]` =

If vec a and vec b are two vectors such that |vec a xxvec b|=2, then find the value of [vec a,vec b,vec a xxvec b]

The position vectors of the points A,B,C , D are respectively 2 vec i + vec j - vec k, vec i + vec j + vec k, vec i- 2 vec j+ 3 vec k and 3 vec i- vec j + 2 vec k . Evaluate [vec (AB), vec (AC), vec (AD)] .

If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a - vec b) * (3 vec a + vec b) .

Evaluate : (3vec(a)-5vec(b)).(2vec(a)+7vec(b)) .

If vec a, and vec b are unit vectors,then find the greatest value of |vec a+vec b|+|vec a-vec b|

Find |vec a| and |vec b|,quad if (vec a+vec b)vec a-vec b=8|vec a|=8|vec b|

Find |vec a| and |vec b|,quad if (vec a-vec b)vec a+vec b=27 and |vec a|=2|vec b|

If vec A, vec B and vec C are mutually perpendicular vectors, then find the value of vec A. vec (B + vec C) .

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

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