To find the area of the Canadian football field, we start with the area of the American football field, which is given as \( 6.4 \times 10^3 \) square yards.
Next, we need to add the difference provided for the Canadian football field:
\[ \text{Area of Canadian football field} = \text{Area of American football field} + 3350 \text{ square yards} \]
Converting \( 3350 \) square yards into scientific notation:
\[ 3350 = 3.35 \times 10^3 \text{ square yards} \]
Now, we can add the two areas:
\[ 6.4 \times 10^3 + 3.35 \times 10^3 = (6.4 + 3.35) \times 10^3 = 9.75 \times 10^3 \text{ square yards} \]
Thus, the area of the Canadian football field is:
\[ \boxed{9.75 \times 10^3} \text{ square yards} \]