If `veca,vecb,vecc and vecd` are unit vectors such that `(vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2` then (A) `veca,vecb,vecc` are non coplanar (B) `vecb,vecc, vecd` are non coplanar (C) `vecb, vecd` are non paralel (D) `veca, vecd` are paralel and `vecb, vecc` 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`