Fluid with \(1040 \mathrm{~kg} / \mathrm{m}^{3}\) density is flowing steadily through the rectangular box shown. Given \(A_{1}=0.046 \mathrm{~m}^{2}, A_{2}=0.009 \mathrm{~m}^{2}\), \(A_{3}=0.056 \mathrm{~m}^{2}, \vec{V}_{1}=3 \hat{i} \mathrm{~m} / \mathrm{s}\) and \(\vec{V}_{2}=6 \hat{j} \mathrm{~m} / \mathrm{s}\), determine velocity \(\vec{V}_{3}\).

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A1 A2 y LX A3 P4.22 -60