If (( a b ) ( c d )) ( a d )=0, then which of the following is always true

Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry

1. \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{~b}}, \overrightarrow{\mathrm{c}}, \overrightarrow{\mathrm{~d}}\) are necessarily coplanar
2. either \(\stackrel{\rightharpoonup}{\mathrm{a}}\) or \(\overrightarrow{\mathrm{d}}\) must lie in the plane of \(\overrightarrow{\mathrm{b}}\) and \(\stackrel{\rightharpoonup}{\mathrm{c}}\)
3. either \(\overrightarrow{\mathrm{b}}\) or \(\stackrel{\rightharpoonup}{\mathrm{c}}\) must lie in plane of \(\stackrel{\rightharpoonup}{\mathrm{a}}\) and \(\overrightarrow{\mathrm{d}}\)
4. either \(\stackrel{\rightharpoonup}{\mathrm{a}}\) or \(\overrightarrow{\mathrm{b}}\) must lie in plane of \(\stackrel{\rightharpoonup}{\mathrm{c}}\) and \(\overrightarrow{\mathrm{d}}\)

Answer

(C) either b or c must lie in plane of a and d

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