AIEEE 2009

JEE Main 2009 Mathematics question on Vector Algebra

If a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} and d⃗\vec{d} are the unit vectors such that (a⃗×b⃗)⋅(c⃗×d⃗)=1(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) = 1 and a⃗⋅c⃗=12\vec{a} \cdot \vec{c} = \frac{1}{2}, then
  1. A.
    a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} are non-coplanar
  2. B.
    a⃗\vec{a}, b⃗\vec{b}, d⃗\vec{d} are non-coplanar
  3. C.
    b⃗\vec{b}, d⃗\vec{d} are non-parallel
  4. D.
    a⃗\vec{a}, d⃗\vec{d} are parallel and b⃗\vec{b}, c⃗\vec{c} are parallel
Show answer

Correct option: C

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