Question
Download Solution PDFबिंदु (2, 3, 4) से रेखा \(\rm \frac{x-0}{1}=\frac{y-0}{0}=\frac{z-0}{0} \ ?\) तक लंबवत दूरी क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
दो लंबवत रेखाओं का बिंदु गुणनफल शून्य है।
दो बिंदुओं (x1, y1, z1) और (x2, y2, z2) के बीच की दूरी निम्न द्वारा दी जाती है, \(\rm \dfrac{x-0}{1}=\dfrac{y-0}{0}=\dfrac{z-0}{0} =k\)
गणना:
माना कि M बिंदु P (2, 3, 4) से खींचे हुए लंब का पाद है
माना कि \(\rm \dfrac{x-0}{1}=\dfrac{y-0}{0}=\dfrac{z-0}{0} =k\)
x = k, y = 0, z = 0
तो M = (k, 0, 0)
अब PM के दिशा अनुपात = (2 - k, 3 - 0, 4 - 0) = (2- k, 3, 4) और दी गई रेखा के दिशा अनुपात 1, 0, 0 हैं।
PM दी गई रेखा के लंबवत है,
(2 - k) (1) + 3(0) + 4 (0) = 0
∴ k = 2
M = (2, 0, 0)
लम्बवत दूरी PM =
\(\rm \sqrt {(2-2)^2+(0-3)^2+(0-4)^2}\\ =\sqrt{9+16}\\ =5\)
इसलिए, विकल्प (2) सही है।
Last updated on May 30, 2025
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