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Question
Find the point on y-axis which is at a distance of \[\sqrt{10}\] units from the point (1, 2, 3).
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Solution
We know that the x and z coordinates of the point on the y-axis are 0.
So, let the required point be (0, y, 0)
Now,
\[\sqrt{\left( 1 - 0 \right)^2 + \left( 2 - y \right)^2 + \left( 3 - 0 \right)^2} = \sqrt{10}\]
\[ \Rightarrow 1 + 4 - 4y + y^2 + 9 = 10\]
\[ \Rightarrow y^2 - 4y + 4 = 0\]
\[ \Rightarrow \left( y - 2 \right)^2 = 0\]
\[ \Rightarrow y = 2, 2\]
Hence, the required point is (0, 2, 0)
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