રેખાઓ $_r^ \to \, = \,\,\left( {\hat i\,\, + \,\,\hat j\,\, - \,\,\hat k\,} \right)\,\, + \,\,\lambda \,\,\left( {2\hat i\,\, - \,\,\hat j\,\, - \,\,\hat k} \right)$ અને $_r^ \to \, = \,\,\left( {\hat i\,\, - \,\,\hat j\,\, - \,\,\hat k\,} \right)\, + \,\,\mu \,\left( i \right)$ વચ્ચેનું લઘુતમ અંતર મેળવો
- A
$2\sqrt 2 $
- B
$\,1/\sqrt 2 $
- ✓
$\sqrt 2 $
- D
✓
Answer
Correct option: C.$\sqrt 2 $
c
$\begin{array}{l}\,\,S.D\,\, = \,\,\frac{{\left( {{{\overline a }_2}\,\, - \,\,{{\overline a }_1}\,} \right)\,\,.\,\,\left( {{{\overline b }_1}\,\, \times \,\,{{\overline b }_2}} \right)\,}}{{|{{\overline b }_1}\,\, \times \,\,{{\overline b }_2}|}}\,\,\\{\overline b _1}\,\, \times \,\,{\overline b _2}\,\, = \,\,i\,\, \times \,\,\left( {2\hat i\,\, - \,\,\hat j\,\, - \,\,\hat k} \right)\, = \,\,2\hat i\,\, \times \,\hat i\,\, - \hat i\,\, \times \,\,\,\hat j\,\, - \,\,\hat i \times \,\,\hat k\,\, = \,\, - \,\,\hat k\,\, + \,\,\,\hat j\\\left( |{{{\overline b }_1}\,\, \times \,\,{{\overline b }_2}} \right|)\,\, = \,\,\sqrt 2\,\,;\,\, \,\,\,{\overline a _2}\,\, - \,\,{\overline a _1}\,\,\, = \,\, - 2\hat j\\S.D\,\, = \,\,\frac{{ - 2\hat j\,.\,\left( {\hat j\,\, - \,\,\hat k} \right)}}{{|\sqrt {2|} }}\,\, = \,\,\left| {\frac{{ - 2}}{{\sqrt 2 }}} \right|\,\, = \,\,\sqrt 2 \end{array}$
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