Question
Download Solution PDFसदिश \(\vec b = \vec i + 2\vec j + \hat k\) पर सदिश \(\vec a = 2\hat i + 3\hat j + 2\hat k\) के प्रक्षेपण का पता लगाएं।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
- अन्य सदिश \(\vec b\) पर एक सदिश \(\vec a\)का प्रक्षेपण इस प्रकार दिया गया है: \(\vec a \cdot \hat b = \frac{\vec a \cdot \vec b}{|\vec b|}\)
गणना:
दिया हुआ: \(\vec a = 2\hat i + 3\hat j + 2\hat k\) और \(\vec b = \vec i + 2\vec j + \hat k\)
यहां, हमें अन्य सदिश \(\vec b\) पर एक सदिश \(\vec a\)का प्रक्षेपण ढूंढना होगा जो इस प्रकार दिया गया है: \(\vec a \cdot \hat b = \frac{\vec a \cdot \vec b}{|\vec b|}\)
⇒ \(\vec a \cdot \vec b = 2 + 6 + 2 = 10 \ and \ |\vec b| = \sqrt {6}\)
⇒ \(\vec a \cdot \hat b = \frac{10}{\sqrt {6}} = \frac{5\sqrt6}{3}\)
इसलिए, विकल्प 3 सही है।
Last updated on Jun 20, 2025
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