Question
Download Solution PDF\(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) మధ్య కోణం \(\vec{a}\) ప్రొజెక్షన్ \(\vec{b}\) -2, ఉంటే అప్పుడు \(|\vec{a}|=\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFపద్ధతి:
\(\rm \vec{a}\) ప్రొజెక్షన్ అయిన \(\rm \vec{b}\) దిశ = \(\rm\dfrac {1}{|\vec b|}(\vec a.\vec b)\)
సాధన:
ఇచ్చిన కోణం \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) మరియు ప్రొజెక్షన్ \(\vec{a}\) \(\vec{b}\)యొక్క దిశ -2
సమాచారం ప్రకారం,
\(\vec{a}\) ప్రొజెక్షన్ అయిన \(\rm \vec{b}\)= \(\rm\dfrac {1}{|\vec b|}(\vec a.\vec b)\) యొక్క దిశ
⇒ - 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 = \(\rm |\vec a|\;(\dfrac {-1}{2})\)
⇒ \(\rm |\vec a| = 4\)
కావునn \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) మధ్యకోణం \(\vec{a}\) ప్రొజెక్షన్ అయిన \(\vec{b}\) దిశ -2, అయిన \(|\vec{a}|=\) 4
Last updated on May 30, 2025
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