Comprehension

निर्देश: निम्नलिखित प्रश्नों के लिए निम्नलिखित को ध्यान में रखें:

माना 2x2 + 2y2 + 2z2 + 3x + 3y + 3z - 6 = 0 एक गोला है।

गोले का व्यास क्या है?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. \(\frac{5\sqrt3}{4}\)
  2. \(\frac{5\sqrt3}{2}\)
  3. \(\frac{3\sqrt5}{4}\)
  4. \(\frac{3\sqrt5}{2}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{5\sqrt3}{2}\)
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NDA 01/2025: English Subject Test
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Detailed Solution

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व्याख्या:

दिया गया है:

गोला: 2x2 + 2y2 + 2z2 + 3x + 3y + 3z - 6 = 0

\(x^2 + y^2+z^2 + \frac{3}{2}x +\frac{3}{2}y + \frac{3}{2}z\) -3 = 0

अब त्रिज्या = \(\sqrt{(\frac{3}{4})^2+ (\frac{3}{4})^2+ (\frac{3}{4})^2 + 3}\)

= \(\sqrt{\frac{27}{16} +3} = \frac{5\sqrt3}{4}\)

व्यास = \(\frac{5\sqrt3}{2}\)

∴ विकल्प (b) सही है

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