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If the line (x−1)/2 = (y+1)/3 = (z−2)/4 meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is:

1. √5/2
2. 2√5
3. 9/2
4. 7/2

Correct answer: 9/2

Solution

Point on line: (1+2t, -1+3t, 2+4t). Plug into x+2y+3z=15: 5 + 20t = 15 -> t = 1/2, giving P = (2, 1/2, 4). Distance from origin = sqrt(4 + 1/4 + 16) = sqrt(81/4) = 9/2.

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