Question
Download Solution PDFComprehension
Direction: Consider the following for the items that follow:
Let 2x2 + 2y2 + 2z2 + 3x + 3y + 3z - 6 = 0 be a sphere.
What is the diameter of the sphere?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
Sphere: 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
Now Radius = \(\sqrt{(\frac{3}{4})^2+ (\frac{3}{4})^2+ (\frac{3}{4})^2 + 3}\)
= \(\sqrt{\frac{27}{16} +3} = 5 \frac{\sqrt3}{4}\)
Diamter = \(5 \frac{\sqrt3}{2}\)
∴ Option (b) is correct
Last updated on May 30, 2025
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