Explain how to subtract vector quantities.

To subtract vector quantities, you add the opposite (negative) of the vector you want to subtract to the original vector.

In more detail, vector subtraction involves a process similar to vector addition, but instead of adding the second vector, you add its opposite. This is because subtracting a vector is the same as adding its negative. For instance, if you have two vectors A and B and you want to find A - B, you would add -B to A.

To do this, you first need to find the negative of the vector you want to subtract. The negative of a vector is a vector of the same magnitude but in the opposite direction. For example, if vector B points to the right, -B would point to the left. If B is 5 units long, -B would also be 5 units long, just in the opposite direction.

Once you have the negative of the vector you want to subtract, you can add it to the original vector. This is done by placing the tail of the second vector at the head of the first vector, then drawing a new vector from the tail of the first vector to the head of the second vector. This new vector is the result of the subtraction.

In terms of components, if you have vectors A = (Ax, Ay) and B = (Bx, By), the subtraction A - B would be done by subtracting the components of B from the components of A, resulting in a new vector (Ax - Bx, Ay - By).

Remember, vectors are quantities that have both magnitude and direction. Therefore, when subtracting vectors, it's important to consider both of these aspects. The magnitude of the resulting vector can be found using Pythagoras' theorem, and the direction can be found using trigonometric functions, typically the tangent function.

In summary, subtracting vector quantities involves finding the negative of the vector to be subtracted and adding it to the original vector, considering both the magnitude and direction of the vectors.