Question
Download Solution PDFमाना कि दो इकाई सदिशों \(\rm \vec a\ और\ \vec b\) के बीच का कोण θ है। यदि \(\rm \vec a+2\vec b\), \(\rm 5\vec a-4\vec b\) के लंबवत है, तो cos θ + cos 2θ किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है:
\(⃗ a+2⃗ b\) और \(\rm 5⃗ a-4⃗ b\) लंबवत सदिश हैं।
⇒ \((⃗ a+2⃗ b).\)\((\rm 5⃗ a-4⃗ b)\) = 0
⇒ \(5|⃗ a|^2 -4⃗ a.⃗ b + 10⃗ a . ⃗ b - 8(⃗ b)^2=0\)
⇒ \(5× 1 + 6⃗ a.⃗ b-8 =0\)
अब \(\vec a, \vec b\) इकाई सदिश हैं
⇒ \(6 |\vec a||\vec b| Cosθ = 3\)
⇒ 6 cosθ = 3
⇒Cosθ = 1/2
अब
cos2 θ = 2Cos2θ -1
= 2x (1/2)2 -1
= \(-\frac{1}{2}\)
अब,
cosθ + cos2θ = 1/2 -1/2 =0
∴ सही उत्तर विकल्प a है
Last updated on Jun 18, 2025
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