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The point P = (4, 2, 7) is reflected in the line L: r = (1, 0, 2) +…
Question
The point P = (4, 2, 7) is reflected in the line L: r = (1, 0, 2) + t(2, 1, 2) to obtain the point P'. Find the sum of the coordinates of P'.
✓ Verified answer: 13checked by our engine — not a guess
Step-by-step solution
Find the foot F of the perpendicular from P to L: F = A + t·d with d·(F - P) = 0.
A - P = (-3, -2, -5). d·(A - P) = -6 - 2 - 10 = -18; d·d = 4 + 1 + 4 = 9. So t = 18/9 = 2.
F = (1 + 4, 0 + 2, 2 + 4) = (5, 2, 6).
The reflection is P' = 2F - P = (10 - 4, 4 - 2, 12 - 7) = (6, 2, 5).
Sum of coordinates = 6 + 2 + 5 = 13.
Final answer13
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