jee-advanced 2009 Q26

jee-advanced · India · paper1 Vector Product and Surfaces
If $\vec { a } , \vec { b } , \vec { c }$ and $\vec { d }$ are unit vectors such that
$$( \vec { a } \times \vec { b } ) \cdot ( \vec { c } \times \vec { d } ) = 1$$
and $\quad \vec { a } \cdot \vec { c } = \frac { 1 } { 2 }$,
then
If $\vec { a } , \vec { b } , \vec { c }$ and $\vec { d }$ are unit vectors such that

$$( \vec { a } \times \vec { b } ) \cdot ( \vec { c } \times \vec { d } ) = 1$$

and $\quad \vec { a } \cdot \vec { c } = \frac { 1 } { 2 }$,

then