Question
Download Solution PDFयदि एक त्रिभुज ABC के शीर्ष A,B,C क्रमशः (1, 1, 3), (-1, 0, 0),(0, 1, 2) है, तो ∠ABC निर्धारित करें। (∠ABC सदिश \(\overrightarrow {BA} \) और \(\overrightarrow {BC} \)के बीच का कोण है)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
त्रिभुज ABC के शीर्ष A,B,C क्रमशः (1, 1, 3), (-1, 0, 0),(0, 1, 2) है।
संकल्पना:
\(\vec{PQ}\) = p.v.(\(\vec{Q}\)) - p.v.(\(\vec{P}\))
सूत्र:
दो सदिश \(\vec{P}\) और \(\vec{Q}\) के बीच का कोण निम्न द्वारा दिया जाता है :
\(\theta = cos^{-1}(\frac{\vec{P}.\vec{Q}}{PQ})\)
हल:
\(\overrightarrow {BA} \) = (1, 1, 3) - (-1, 0, 0)
= 2î + ĵ + 3k̂
\(\overrightarrow {BC} \) = (0, 1, 2) - (-1, 0, 0) = î + ĵ + 2k̂
∴ \(\theta = cos^{-1}(\frac{\vec{BA}.\vec{BC}}{BA.BC})\)
\(\Rightarrow \theta = cos^{-1}(\frac{9}{\sqrt 14 \sqrt 6})\))
\(\Rightarrow \theta ={{\mathop{\rm cos}\nolimits} ^{ - 1}}(\frac{9}{{\sqrt 84}})\)
Last updated on Jun 19, 2025
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