To determine the direction of the vector resulting from subtracting [tex]\( A \)[/tex] (which points north) from [tex]\( B \)[/tex] (which points east), we need to consider their components in a 2D coordinate plane.
1. Representing the vectors:
- Vector [tex]\( A \)[/tex] (north) can be represented as [tex]\( (0, 1) \)[/tex]. This is because north corresponds to a movement in the positive y-direction.
- Vector [tex]\( B \)[/tex] (east) can be represented as [tex]\( (1, 0) \)[/tex]. This is because east corresponds to a movement in the positive x-direction.
2. Subtracting the vectors:
- To find [tex]\( \mathbf{B} - \mathbf{A} \)[/tex], we subtract the components of [tex]\( \mathbf{A} \)[/tex] from the components of [tex]\( \mathbf{B} \)[/tex]:
[tex]\[
(1, 0) - (0, 1) = (1 - 0, 0 - 1) = (1, -1)
\][/tex]
3. Interpreting the result:
- The vector [tex]\( (1, -1) \)[/tex] shows a movement of 1 unit in the positive x-direction (east) and 1 unit in the negative y-direction (south). When we combine these two components, the resulting vector points diagonally in the direction that is south of east.
Thus, after performing the subtraction and analyzing the resulting vector, we find that the direction of the vector [tex]\( \mathbf{B} - \mathbf{A} \)[/tex] is south of east.
The correct answer is b. south of east.
