Given the 3 dimensional electric field, \(\vec{E}\) = 200 \(\frac{N}{C}\) \(\hat{i}\) + 300 \(\frac{N}{C}\) \(\hat{j}\) + 400 \(\frac{N}{C}\) \(\hat{k}\) , and an area vector \(\vec{A}\) = 0.2 m\(^2\) \(\hat{i}\) + 0.3 m\(^2\) \(\hat{j}\), find the electric flux. (this is a calculus based physics problem)
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