In practice, the similarities between working a vector addition problem and a vector subtraction problem should be striking. In both cases, you will make a vector diagram, choose a coordinate system, and break your vectors up into components. The only real difference between the two is whether you add the components together or subtract them. However you combine them, remember that you only want to combine x components with x components and y components with y components.

The other difference between vector addition problems and vector subtraction problems that can cause mistakes is the order of your vectors. In a vector addition problem, the order doesn’t matter. [latex]\vec{A}+\vec{B}[/latex] is the same as [latex]\vec{B}+\vec{A}[/latex]. However, order does matter in vector subtraction. The vector [latex]\vec{A}-\vec{B}[/latex] points in the opposite direction as the vector [latex]\vec{B}-\vec{A}[/latex]. When you are calculating the change in a vector quantity, make sure you always subtract the initial vector from the final vector, and not the other way around.