Question
Download Solution PDFযদি \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) এবং \(\vec{b}\) এর দিকে \(\vec{a}\) এর অভিক্ষেপ -2 হয়, তাহলে \(|\vec{a}|=\) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFধারণা:
\(\rm \vec{b}\) এর দিকে \(\rm \vec{a}\) এর অভিক্ষেপ = \(\rm\dfrac {1}{|\vec b|}(\vec a.\vec b)\)
গণনা:
প্রদত্ত, \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) এবং \(\vec{a}\) এর অভিক্ষেপের দিক থেকে \(\vec{b}\) হল -2
আমরা জানি যে,
\(\rm \vec{b}\) এর দিকে \(\rm \vec{a}\) এর অভিক্ষেপ = \(\rm\dfrac {1}{|\vec b|}(\vec a.\vec b)\)⇒ - 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 = \(\rm |\vec a|\;(\dfrac {-1}{2})\)
⇒ \(\rm |\vec a| = 4\)
তাই, যদি \(\rm \vec{a} \ and \ \vec{b} \ is \ \dfrac{2\pi}{3}\) এবং \(\vec{b}\) এর দিকে \(\vec{a}\) এর অভিক্ষেপ -2 হয়, তাহলে \(|\vec{a}|=\) 4
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