If a b = c d and a c = b d and a d , ~b c , Then
Mathematics · JEE Main · NTA Exams — Three Dimensional Geometry
If \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{d}}\) and \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{d}} \text { and } \overrightarrow{\mathrm{a}} \neq \overrightarrow{\mathrm{d}}, \overrightarrow{\mathrm{~b}} \neq \overrightarrow{\mathrm{c}},\) Then
- \(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{d}}\) is parallel to \(\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}}\).
- \(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{d}}\) is perpendicular to \(\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}}\).
- \(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{d}}\) is equal to \(\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}}\).
- none of these
Answer
(A) a - d is parallel to b - c .
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