Let `vec(X),vec(Y)` and `vec(Z)` be three vectors such that `|vec(X)|=|vec(Y)|=|vec(Z)|=sqrt(2)`. The angle between `vec(X),vec(Y)` and `vec(Z)` with each other `60^(@)`. `vec(X)xx(vec(Y)xx vec(Z))=vec(a),vec(Y)xx(vec(Z)xx vec(X))=vec(b)` and `vec(X)xx vec(Y)=vec( C )`
Vector `vec(Z)` = ............. .

Options

A. `(1)/(2){(vec(b)-vec( c ))xx vec( c )+(vec(a)+vec(b))}`
B. `(1)/(2){(vec(b)-vec(a))+(vec(a)+vec(b))xx vec( c )}`
C. `{(vec(b)-vec(a))xx vec( c )+(vec(a)+vec(b))}`
D. None of these