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Question
Find the coordinates of points on line `x/1 = (y - 1)/2 = (z + 1)/2` which are at a distance of `sqrt(11)` units from origin.
Solution
Given line is
`x/1 = (y - 1)/2 = (z + 1)/2` = k (assume)
x = k, y = 2k + 1, z = 2k – 1
So, let point on the given line is
P(k, 2k + 1, 2k – 1)
Distance of point (P) from the origin is
`sqrt((k - 0)^2 + (2k + 1 - 0)^2 + (2k - 1 - 0)^2`
Now `sqrt(k^2 + (2k + 1)^2 + (2k - 1)^2) = sqrt(11)` ...(Given)
`\implies` k2 + 4k2 + 1 + 4k + 4k2 + 1 – 4k = 11
`\implies` 9k2 + 2 = 11
`\implies` 9k2 = 9
`\implies` k = ± 1
Therefore, point on the line is (1, 3, 1) or (– 1, – 1 – 3).
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