Question
Download Solution PDFउस बिंदु का निर्देशांक ज्ञात कीजिए जहाँ बिंदु A (2, 3, 2) और B (5, 1, 6) से होकर गुजरने वाली रेखा XY - तल को पार करती है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
A(2, 3, 2) और B(5, 1, 6) दो बिंदु हैं।
संकल्पना:
A(x1, y1, z1) और B(x2, y2, z2) से होकर गुजरने वाली एक रेखा के काटीज़ियन समीकरण को निम्न द्वारा ज्ञात किया गया है,
\(\frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} = \frac{z - z_1}{z_2- z_1}\)
गणना:
यहाँ, x1 = 2, y1 = 3, z1 = 2, x2 = 5, y2 = 1 और z2 = 6
आवश्यक रेखा का काटीज़ियन समीकरण निम्न है:
⇒ \(\frac{x - 2}{5 - 2} = \frac{ y - 3}{1 -3} = \frac{z - 2}{6 - 2}\)
⇒ \(\frac{ x - 2}{3} = \frac{ y - 3}{-2} = \frac{ z - 2}{4}\) ---- समीकरण (1)
रेखा xy - तल अर्थात् z = 0 को पार करता है।
इसलिए, समीकरण (1) में z = 0 रखने पर, हमें निम्न प्राप्त होता है
⇒ \(\frac{ x - 2}{3} = \frac{ y - 3}{-2} = \frac{ 0 - 2}{4}\)
⇒ \(\frac{ x - 2}{3} = \frac{ y - 3}{-2} = \frac{-1}{2}\)
⇒ \(\frac{ x - 2}{3} = \frac{-1}{2}\) और \( \frac{ y - 3}{-2} = \frac{-1}{2} \)
⇒ 2x - 4 = - 3 और 2y - 6 = 2
⇒ 2x = 1 और 2y = 8
⇒ x = \(\frac{1}{2}\) और y = 4
∴ रेखा AB, (1/2, 4. 0) पर XY - तल को पार करता है।
Last updated on Jun 19, 2025
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