Draw the standard basis vectors $\hat\imath$, $\hat\jmath$, $\hat{k}$ co-directional to the two parts of the water main given

Question

A water main is to be constructed with a $20.0$​% grade in the north direction and a $10$​% grade in the east direction. Determine the angle $\theta$ required in the water main for the turn from north to east. SOLUTION:

I'm not sure why the vector parallel to the north doesn't have a j component while the vector to the east has a j component and no i component.

I'm wondering how to draw the axis, the vectors of the basis or some coordinates so I can know what direction their $\hat\imath$, $\hat\jmath$, $\hat{k}$ point basis vectors point. I doubt that the standard basis is being used.

Is East in the direction of $\hat\imath$? Did change of basis happen here? East and North the cardinal directions appear distorted visually.

Answer 1

Hint: $\hat{i}$ points in the direction of south.