Vector Subtraction in Components

Vector subtraction in components

When vectors are written in component form, subtract them component by component. The main idea is that each coordinate is handled separately.

Method

1. Write the vectors in matching order, such as ((a, b) - (c, d)).
2. Subtract the first components: (a - c).
3. Subtract the second components: (b - d).
4. Simplify each result.
5. Write the final vector in component form.

Important note

Be careful with negative signs. Subtracting a vector means you subtract every component of the second vector, not just the first one.

Example pattern

[(x_1, y_1) - (x_2, y_2) = (x_1 - x_2,; y_1 - y_2)]

Quick check

To verify your answer, add the vector you subtracted back to your result. If the sum gives the original first vector, your subtraction is correct.

Common mistake to avoid

Do not combine components across positions. The first coordinate only works with the first coordinate, and the second with the second.