Question
Download Solution PDFसमतलों x = 3z + 4 और y = 2z - 3 के प्रतिच्छेदन की रेखा के दिशा अनुपात क्या हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
दिशा अनुपात (a, b, c) के साथ एक रेखा का समीकरण, जो बिंदु (x1, y1, z1) से होकर गुजरती है, निम्न सूत्र द्वारा दिया गया है: \(\rm \frac{{x - {x_1}}}{a} = \frac{{y - {y_1}}}{b} = \frac{{z - {z_1}}}{c}\)
यदि दो समतल एक -दूसरे को प्रतिच्छेदित करते हैं तो प्रतिच्छेदन हमेशा एक रेखा होगा।
गणना:
दिया हुआ:
x = 3z + 4 और y = 2z - 3
⇒ x - 4 = 3z और y + 3 = 2z
\(\rm \Rightarrow \frac{x - 4}{3} = z \;\text{and} \ \frac{y + 3}{2} = z\)
\(\rm \Rightarrow \frac{x - 4}{3} = \frac{y + 3}{2} = \frac{z}{1}\)
यदि दो समतल एक -दूसरे को प्रतिच्छेदित करते हैं तो प्रतिच्छेदन हमेशा एक रेखा होगा।
अब, रेखा के दिशा अनुपात 〈3, 2, 1〉 हैं
Last updated on May 31, 2025
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