If ${{l}_{1}},\,{{m}_{1}},\,{{n}_{1}}$ and ${{l}_{2}},{{m}_{2}},{{n}_{2}}$ are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be

Question

Accepted Answer

$({{m}_{1}}{{n}_{2}}-{{m}_{2}}{{n}_{1}}),\,\,({{n}_{1}}{{l}_{2}}-{{n}_{2}}{{l}_{1}}),\,({{l}_{1}}{{m}_{2}}-{{l}_{2}}{{m}_{1}})$

Answer

$({{l}_{1}}{{l}_{2}}-{{m}_{1}}{{m}_{2}}),\,({{m}_{1}}{{m}_{2}}-{{n}_{1}}{{n}_{2}}),\,({{n}_{1}}{{n}_{2}}-{{l}_{1}}{{l}_{2}})$

Answer

$\frac{1}{\sqrt{l_{1}^{2}+m_{1}^{2}+n_{1}^{2}}},\frac{1}{\sqrt{l_{2}^{2}+m_{2}^{2}+n_{2}^{2}}},\frac{1}{\sqrt{3}}$

Answer

$\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$

3-d

Question: If ${{l}_{1}},\,{{m}_{1}},\,{{n}_{1}}$ and ${{l}_{2}},{{m}_{2}},{{n}_{2}}$ are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be

3-d

Question: If ${{l}_{1}},\,{{m}_{1}},\,{{n}_{1}}$ and ${{l}_{2}},{{m}_{2}},{{n}_{2}}$ are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be

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