Question
Download Solution PDFसदिश \(\left( {\vec i + \lambda \vec j + 3\vec k} \right)\)और \(\left( {3\vec i + 2\vec j + 9\vec k} \right)\)में λ का मान क्या है जो समानांतर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिए गए दो सदिश समानांतर है, इसलिए इन दो सदिश का सदिश गुणनखंड शून्य होगा।
\(\vec a\parallel \vec b \Leftrightarrow \vec a \times \vec b = \vec 0\)
\(\Rightarrow \left| {\begin{array}{*{20}{c}} {\hat i}&{\hat j}&{\hat k}\\ 1&\lambda &3\\ 3&2&9 \end{array}} \right| = 0\)
\(= \left( {9\lambda - 6} \right)\hat i - \left( {9 - 9} \right)\hat j + \left({2 - 3\lambda} \right)\hat k = \vec 0\)
⇒ 9λ – 6 = 0 और 2 - 3λ = 0
∴ λ = 2/3Last updated on Jun 26, 2025
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