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A line ℓ passing through the origin is perpendicular to the lines ℓ₁: (3 + t) i + (-1 + 2t) j + (4 + 2t) k, -∞ < t < ∞ ℓ₂: (3 + 2s) i + (3 + 2s) j + (2 + s) k, -∞ < s < ∞ Then the coordinates(s) of the point(s) on ℓ₂ at a distance of √17 from the point of intersection of ℓ and ℓ₁ is(are)

1. (7/3, 7/3, 5/3)
2. (-1, -1, 0)
3. (1, 1, 1)
4. (7/9, 7/9, 8/9)

Correct answer: (-1, -1, 0)

Solution

The line ℓ is perpendicular to ℓ₁, and its intersection point with ℓ₁ is determined. Using the distance condition of √17 from this point, the coordinates on ℓ₂ are calculated as (-1, -1, 0).

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