Question
Download Solution PDFयदि \(\left| {\overrightarrow a } \right|\) = \(\left| {\overrightarrow b } \right|\) = \(\left| {\overrightarrow c } \right|\) और \(\overrightarrow a \, + \,\overrightarrow b \, = \,\,\overrightarrow c \) है, तो \(\overrightarrow a \) और \(\overrightarrow b \) के बीच का कोण ____ है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFहमारे पास है,
यदि, \(\left| {\overrightarrow a } \right|\) = \(\left| {\overrightarrow b } \right|\) = \(\left| {\overrightarrow c } \right|\)
⇒ a = b = c .... (1)
और,
\(\overrightarrow a \, + \,\overrightarrow b \, = \,\,\overrightarrow c \) .... (2)
सदिश योग के समांतर चतुर्भुज नियम की अवधारणा का उपयोग करते हुए: इसका उपयोग दो सदिश राशियों को जोड़ने के लिए किया जाता है।
\(\overrightarrow A \, + \,\overrightarrow B \, = \,\,\overrightarrow R\)
R2 = A2 + B2 +2AB cos θ
समीकरण (2) से,
c2 = a2 + b2 +2ab cos θ
तब से,
a = b = c
अत,
a2 = a2 + a2 +2a2 cos θ
या, a2 = a2 (1 + 1 +2cos θ)
या, 1 = 2 + 2 cos θ
या, 2 cos θ = -1
या, cos θ = (-0.5)
इसलिए, θ = cos-1 (0.5) = 120° = \(\frac{{2\pi }}{3}\)
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