Word Count : 739

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आइए एक-एक करके सभी कथनों का संख्यात्मक रूप से विश्लेषण करते हैं और सत्य/असत्य का निर्णय करते हैं: --- ### (i) संख्याएँ $$ \frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\frac{3}{4} $$ एक रेखा की दिक्कोज्याएं हैं। दिक्कोज्याओं का वर्गों का योग 1 होना चाहिए: $$ \left(\frac{1}{\sqrt{2}}\right)^2 + \left(\frac{1}{\sqrt{3}}\right)^2 + \left(\frac{3}{4}\right)^2 = \frac{1}{2} + \frac{1}{3} + \frac{9}{16} $$ सामान्य हर लें: $$ \frac{1}{2} = \frac{24}{48}, \quad \frac{1}{3} = \frac{16}{48}, \quad \frac{9}{16} = \frac{27}{48} \Rightarrow \frac{24+16+27}{48} = \frac{67}{48} > 1 $$ ➡️ सत्य नहीं। ✅ उत्तर: असत्य कारण: दिक्कोज्याओं के वर्गों का योग 1 से अधिक है। --- ### (ii) बिंदु (1,2), (7,6), (4,4) संरेखीय हैं। तीनों बिंदु एक ही रेखा पर होंगे यदि उनके बीच की ढालें समान हों। ढाल 1 और 2 के बीच: $$ m_1 = \frac{6 - 2}{7 - 1} = \frac{4}{6} = \frac{2}{3} $$ ढाल 1 और 3 के बीच: $$ m_2 = \frac{4 - 2}{4 - 1} = \frac{2}{3} ______ _____ ____ ____ _____.
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