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To find the magnitude of the resultant displacement (\mathbf{R} = \mathbf{A} + \mathbf{B}), we first add the vectors:

[ \mathbf{R} = (5i - 23) + (-3i + 4j + 6k) = (5 - 3)i + 4j + 6k - 23 = 2i + 4j + 6k - 23. ]

This simplifies to (\mathbf{R} = 2i + 4j - 17). The magnitude of (\mathbf{R}) is given by:

[ |\mathbf{R}| = \sqrt{(2)^2 + (4)^2 + (-17)^2} = \sqrt{4 + 16 + 289} = \sqrt{309} \approx 17.578. ]

Thus, the magnitude of the resultant displacement is approximately 17.58 m.

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