Question
Download Solution PDFयदि \(|\vec a|\) = 3, \(\left| {\vec b} \right| = 4\) और \(\left| {\vec a - \vec b} \right| = 5,\) तो \(\left| {\vec a + \vec b} \right|\) का मूल्य क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
- \({\left| {\vec a - \vec b} \right|^2} + \;{\left| {\vec a + \vec b} \right|^2} = \;2\; \times \;\left( {{{\left| {\vec a} \right|}^2} + \;{{\left| {\vec b} \right|}^2}} \right)\)
गणना:
दिया हुआ: \(|\vec a|\) = 3, \(\left| {\vec b} \right| = 4\) और \(\left| {\vec a - \vec b} \right| = 5,\)
हम जानते हैं कि,
\({\left| {\vec a - \vec b} \right|^2} + \;{\left| {\vec a + \vec b} \right|^2} = \;2\; \times \;\left( {{{\left| {\vec a} \right|}^2} + \;{{\left| {\vec b} \right|}^2}} \right)\)
\(\Rightarrow {5^2} + \;{\left| {\vec a + \vec b} \right|^2} = \;2\; \times \;\left( {{3^2} + \;{4^2}} \right)\)
\(\Rightarrow {\left| {\vec a + \vec b} \right|^2} = \;50 - 25 = 25\)
∴ \(\left| {\vec a + \vec b} \right| = 5\)
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