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Question
Let (3, 4, –1) and (–1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to
Options
2
3
6
7
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Solution
3
Suppose d is the diameter of the sphere. Then
\[d^2 = \left( - 1 - 3 \right)^2 + \left( 2 - 4 \right)^2 + \left( 3 + 1 \right)^2 \]
\[ \Rightarrow d^2 = \left( - 4 \right)^2 + \left( - 2 \right)^2 + \left( 4 \right)^2 \]
\[ \Rightarrow d^2 = 16 + 4 + 16\]
\[ \Rightarrow d^2 = 36\]
\[ \Rightarrow d = 6\]
Hence, radius of the sphere is 3 units.
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