Math Help - Using Cartesian Vectors

1. Using Cartesian Vectors

How would I solve the question below using Cartesian vectors?

10. A plane is flying southeast at a constant speed of 900 km/h. The wind is blowing towards the north at 100 km/h. Determine the resultant velocity of the plane relative to the ground.

How would I do this? I can use geometric vectors and get the correct answer and angle, but the the Cartesian vectors.

2. Originally Posted by Barthayn
How would I solve the question below using Cartesian vectors?

10. A plane is flying southeast at a constant speed of 900 km/h. The wind is blowing towards the north at 100 km/h. Determine the resultant velocity of the plane relative to the ground.

How would I do this? I can use geometric vectors and get the correct answer and angle, but the the Cartesian vectors.
air vector , $\vec{A} = 450\sqrt{2} \cdot \vec{i} - 450\sqrt{2} \cdot \vec{j}$

wind vector, $\vec{W} = 100 \vec{j}$

ground vector, $\vec{G} = \vec{A} + \vec{W}$

3. I figured out my mistake, I thought the wind speed was 10 km/h. Thanks for your aid, however, what is i and j?

4. Originally Posted by Barthayn
... however, what is i and j?
i and j are the respective unit vectors in the x and y directions.