Step 1: Calculate the magnitude of the force of the wrench:
Given \( \vec{F} = 500\hat{i} + 300\hat{j} + 800\hat{k} \), the magnitude of the force is:
\[ |\vec{F}| = \sqrt{500^2 + 300^2 + 800^2} = \sqrt{250000 + 90000 + 640000} = \sqrt{980000} = 990 \text{ N} \]
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