The direction cosines of three lines passing through the origin are ${{l}_{1}},{{m}_{1}},{{n}_{1}};\,{{l}_{2}},{{m}_{2}},{{n}_{2}}$and ${{l}_{3}},{{m}_{3}},{{n}_{3}}$. The lines will be coplanar, if

Question

Accepted Answer

$\begin{vmatrix} {{l_1}}&{{n_1}}&{{m_1}}\ {{l_2}}&{{n_2}}&{{m_2}}\ {{l_3}}&{{n_3}}&{{m_3}} \end{vmatrix} = 0$

Answer

$\begin{vmatrix} {{l_1}}&{{m_2}}&{{n_3}}\ {{l_2}}&{{m_3}}&{{n_1}}\ {{l_3}}&{{m_1}}&{{n_2}} \end{vmatrix} = 0$

Answer

${{l}_{1}}{{l}_{2}}{{l}_{3}}+{{m}_{1}}{{m}_{2}}{{m}_{3}}+{{n}_{1}}{{n}_{2}}{{n}_{3}}=0$

Answer

None of these

3-d

Question: The direction cosines of three lines passing through the origin are ${{l}_{1}},{{m}_{1}},{{n}_{1}};\,{{l}_{2}},{{m}_{2}},{{n}_{2}}$and ${{l}_{3}},{{m}_{3}},{{n}_{3}}$. The lines will be coplanar, if

3-d

Question: The direction cosines of three lines passing through the origin are ${{l}_{1}},{{m}_{1}},{{n}_{1}};\,{{l}_{2}},{{m}_{2}},{{n}_{2}}$and ${{l}_{3}},{{m}_{3}},{{n}_{3}}$. The lines will be coplanar, if

Related Questions