Question
Download Solution PDFयदि P (2, 3, 4), Q (5, 8, 7) और R (-1, -2, 1) संरेख हैं, तो R, PQ को इस अनुपात में विभाजित करता है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
P (2, 3, 4), Q (5, 8, 7) और R (-1, -2, 1) संरेख हैं।
अवधारणा:
यदि x, x1 और x2 को अनुपात m1:m2 में विभाजित करता है
\(\rm x=\frac{m_1x_2+m_2x_1}{m_1+m_2}\)
गणना:
P (2, 3, 4), Q (5, 8, 7) और R (-1, -2, 1) संरेख हैं।
माना R, PQ को k : 1 के अनुपात में विभाजित करता है
और x = -1, x1 = 2 और x2 = 5
तब x निर्देशांक शर्त को संतुष्ट करते हैं
\(\rm x=\frac{kx_2+x_1}{k+1}\)
\(\rm -1=\frac{k(5)+1(2)}{k+1}\)
⇒ - k - 1 = 5k + 2
⇒ 6k = - 3
⇒ k = -1/2
तब अनुपात k : 1 = -1 : 2
अनुपात ऋणात्मक नहीं हो सकता है
इसका मतलब है कि R, PQ को बाह्य रूप से 1:2 के अनुपात में विभाजित करता है।
अतः विकल्प (2) सही है।
Last updated on Jun 17, 2025
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