If a , b , c and are unit vectors such that ( a b ) ( c d )=1 and a c = 1 2 , then

Mathematics · JEE Advanced · NTA ExamsVector Algebra

If \(\vec{a}, \vec{b}, \vec{c}\) and are unit vectors such that \((\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d})=1\) \(\text { and } \vec{a} \cdot \vec{c}=\frac{1}{2} \text {, then }\)
  1. are non-coplanar
  2. are non-coplanar
  3. are non-parallel
  4. are parallel and are parallel

Answer

(D) are parallel and are parallel

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