1)

If ((a×b)×(c×d)).(a×d)=0

then which of the following is always true ?


A) a,b,c,d are necessarily coplanar

B) Either a or d must lie in the plane of b and c

C) Either b or c must lie in the plane of a and d

D) Either a or b must lie in the plane of c and d

Answer:

Option C

Explanation:

((a×b)×(c×d)).(a×d)=0

([acd]b[bcd]a).(a×d)=0

[acd][bad]=0

Either c or b must lie in the plane of a and d