Question
Download Solution PDFयदि \(\vec{a}\) और \(\vec{b}\) के बीच का कोण \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) है और \(\vec{b}\) की दिशा में \(\vec{a}\) का प्रक्षेपण -2 है, तो \(|\vec{a}|=\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\(\rm \vec{b}\) की दिशा में \(\rm \vec{a}\) का प्रक्षेपण = \(\rm\dfrac {1}{|\vec b|}(\vec a.\vec b)\)
गणना:
दिया गया है, \(\vec{a}\) और \(\vec{b}\) के बीच का कोण \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) है और \(\vec{b}\)की दिशा में \(\vec{a}\)का प्रक्षेपण -2 है।
हम जानते हैं कि,
\(\rm \vec{b}\) की दिशा में \(\vec{a}\) का प्रक्षेपण = \(\rm\dfrac {1}{|\vec b|}(\vec a.\vec b)\)
⇒ - 2 = \(\rm\dfrac {1}{|\vec b|}(|\vec a||\vec b|\;cos\;\dfrac {2\pi}{3})\)
⇒ - 2 = \(\rm |\vec a|\;cos\;\dfrac {2\pi}{3}\)
⇒ - 2 = \(\rm |\vec a|\;(\dfrac {-1}{2})\)
⇒ \(\rm |\vec a| = 4\)
अतः यदि \(\vec{a}\) और \(\vec{b}\) के बीच का कोण \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) है और \(\vec{b}\) की दिशा में \(\vec{a}\) का प्रक्षेपण -2 है, तो \(|\vec{a}|=\) 4 है।
Last updated on May 30, 2025
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