To find the area of a Canadian football field, we start with the area of the American football field, which is given as \( 6.4 \times 10^3 \) square yards.
The area of the Canadian football field is \( 3,350 \) square yards larger than that of the American football field. Therefore, we can calculate the area of the Canadian football field as follows:
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Convert \( 3,350 \) to scientific notation: \[ 3,350 = 3.35 \times 10^3 \]
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Now add the area of the American field to the increase: \[ \text{Area of Canadian field} = 6.4 \times 10^3 + 3.35 \times 10^3 \]
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Combine the two quantities: \[ 6.4 \times 10^3 + 3.35 \times 10^3 = (6.4 + 3.35) \times 10^3 = 9.75 \times 10^3 \]
Thus, the area of the Canadian football field is:
\[ \boxed{9.75 \times 10^3} \text{ square yards} \]