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Home » Seeker Seeker: The Epic Journey That’s Shaking the World! - Redraw

Seeker Seeker: The Epic Journey That’s Shaking the World! - Redraw

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Total time: 0.75 + 0.3 = <<0.75 + 0.3 = 1.05>>1.05 hours

📌 #### 22.86Question: Given three points in 3D space representing the positions of three solar panels on a satellite—$ A = (1, 2, 3) $, $ B = (4, 5, 6) $, and $ C = (7, 8, 9) $—find the coordinates of a fourth point $ D $ such that $ ABCD $ forms a parallelogram in space, assuming all coordinates are integers.

📌 Solution: To find point $ D $ such that $ ABCD $ is a parallelogram, we use the property that in a parallelogram, the diagonals bisect each other. Therefore, the midpoint of diagonal $ AC $ must be the same as the midpoint of diagonal $ BD $.

📌 First, compute the midpoint of $ AC $:

📌 Let $ D = (x, y, z) $. Then the midpoint of $ BD $ must also be $ (4, 5, 6) $. Compute the midpoint of $ BD $:

📌 Thus, $ D = (4, 5, 6) $. However, this coincides with point $ B $, which implies $ ABCD $ collapses into a degenerate parallelogram (a line segment), not a valid 3D parallelogram.

📌 Thus, the only point $ D $ satisfying parallelogram vector conditions is $ (4,5,6) $, but it lies on the line through $ A, B, C $, so $ ABCD $ is degenerate.

📌 But the problem allows integer coordinates and does not specify non-degeneracy, so technically:

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