The shortest distance between the skew lines _ 1 : r = a _ 1 + b _ 1 and _ 2 : r = a _ 2…

Mathematics · JEE Main · NTA Exams — Three Dimensional Geometry

1. \[\frac{\left|\left(\overrightarrow{\mathrm{a}}_{2}-\overrightarrow{\mathrm{a}}_{1}\right) \cdot\left(\overrightarrow{\mathrm{b}}_{1} \times \overrightarrow{\mathrm{b}}_{2}\right)\right|}{\left|\overrightarrow{\mathrm{b}}_{1} \times \overrightarrow{\mathrm{b}}_{2}\right|}\]
2. \[\frac{\left|\left(\vec{a}_{2}-\vec{a}_{1}\right) \cdot\left(\vec{a}_{2} \times \vec{b}_{2}\right)\right|}{\left|\vec{b}_{1} \times \vec{b}_{2}\right|}\]
3. \[\frac{\left|\left(\vec{a}_{2}-\vec{b}_{2}\right) \cdot\left(\vec{a}_{1} \times \vec{b}_{1}\right)\right|}{\left|\vec{b}_{1} \times \vec{b}_{2}\right|}\]
4. \[\frac{\left|\left(\vec{a}_{1}-\vec{b}_{2}\right) \cdot\left(\vec{b}_{1} \times \vec{a}_{2}\right)\right|}{\left|\vec{b}_{1} \times \vec{b}_{2}\right|}\]

Answer

(A) | ( a _ 2 - a _ 1 ) ( b _ 1 b _ 2 ) | | b _ 1 b _ 2 |

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