If a, b, c and d are the unit vectors such that (a x b). (c x d) = 1 and a.c = ½, then:

1) a, b, c are non- coplanar

2) a, b, d are non- coplanar

3) b, d are non -parallel

4) a, d are parallel and b, c are parallel

Answer: (3) b, d are non -parallel

Solution: Given,

(a x b). (c x d) = 1, it is possible when,

|a x b|.|c x d| = 1 and (a x c) || ( c x d)

Also, given,

a.c = ½ and if we say, b||d then,

|c x d| ≠ 1

Which is not possible.

Therefore, we can say that b and d are non-parallel.

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