A river is flowing with a velocity of $1 \mathrm{m} {\sec }^{-1}$ toward east direction. When the boat runs with a velocity of $3 \mathrm{m} {\mathrm{s}}^{-1}$ relative to the river in the direction of the river flow, the flag on the boat flutter in the north direction. If the boat runs with the same speed but in the north direction relative to the river, the flag flutters towards the northeast direction. The actual velocity of the wind (relative to the ground) should be: ( $\hat{\mathrm{i}}=$ east direction and $\hat{\mathrm{j}}=$ north direction)