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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2020 · Mathematics · Three Dimensional Geometry

What is the length of the diameter of the sphere whose centre is at...

What is the length of the diameter of the sphere whose centre is at (1,−2,3)(1,-2,3) and which touches the plane 6x−3y+2z−4=06 x-3 y+2 z-4=0 ?

Options

  1. A1 unit
  2. B2 units
  3. C3 units
  4. D4 units

Correct answer

D. 4 units

Step-by-step solution

Radius of the sphere =6(1)−3(−2)+2(3)−4(6)2+(−3)2+(2)2=6+6+6−47=147=2=\frac{6(1)-3(-2)+2(3)-4}{\sqrt{(6)^2+(-3)^2+(2)^2}}=\frac{6+6+6-4}{7}=\frac{14}{7}=2 Diameter of the sphere =2×2=4=2 \times 2=4 units
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