If `vec a, vec b,vec c and vec d` are unit vectors such that `(vec a xx vec b)`.`vec c xx vec d= 1` and `vec a.vec c =1/2` then a) `vec a, vec b and vec c` are non-coplanar b) `vec b, vec c ,vec d` are non -coplanar c)`vec b, vecd` are non parallel d) `vec a , vec d` are parallel and `vec b, vec c ` are parallel

Options

A. `veca, vecb and vecc` are non- coplanar
B. `vecb, vecc and vecd` are non-coplanar
C. `vecb and vecd` are non- parallel
D. `veca and vecd` are parallel and `vecb and vecc` are parallel

Answer

c

Explanation

` (veca xx vecb) . (vecc xx vecd) =1 ` is possible only when
` |veca xx vecb|= |vecc xx vecd|=1 and (veca xx vecb) || (vecc xx vecd)`
since `veca . Vecc = 1/2 and if vecb||vecd , " then " |vecc xx vecd|ne 1`