a¯, b¯, c¯, d¯ be any four vectors then a¯×b¯×c¯×d¯ is vector

a¯×b¯⊥ to a¯,b¯c¯×d¯⊥ to c¯,d¯(a¯×b¯)×(c¯×d¯)⊥ to both a¯×b¯,c¯×d¯⇒(a¯×b¯)×(c¯×d¯) lies along line of intersection of 2 planes.

a¯, b¯, c¯, d¯ be any four vectors then a¯×b¯×c¯×d¯ is vector

a¯×b¯⊥ to a¯,b¯c¯×d¯⊥ to c¯,d¯(a¯×b¯)×(c¯×d¯)⊥ to both a¯×b¯,c¯×d¯⇒(a¯×b¯)×(c¯×d¯) lies along line of intersection of 2 planes.

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$\bar{a}, \bar{b}, \bar{c}, \bar{d}$ be any four vectors then $(\bar{a} \times \bar{b}) \times (\bar{c} \times \bar{d})$ is vector

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$∥^{e^{2}} to \bar{a} \times \bar{b} and ⊥ to \bar{c} \times \bar{d}$

Along the line of intersection of two planes one containing $\bar{a}, \bar{b}$ and the other containing $\bar{c}, \bar{d}$

$⊥$ to $\bar{a} \bar{b} \bar{c} \bar{d}$

$⊥$ to $\bar{a} \times \bar{b}, ∥^{lel} to \bar{c} \times \bar{d}$

answer is D.

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Detailed Solution

$\begin{array}{l} \bar{a} \times \bar{b} ⊥ to \bar{a}, \bar{b} \\ \bar{c} \times \bar{d} ⊥ to \bar{c}, \bar{d} \\ (\bar{a} \times \bar{b}) \times (\bar{c} \times \bar{d}) ⊥ to both \bar{a} \times \bar{b}, \bar{c} \times \bar{d} \end{array}$
$\Rightarrow (\bar{a} \times \bar{b}) \times (\bar{c} \times \bar{d})$ lies along line of intersection of 2 planes.