# High School: Number and Quantity

### Vector and Matrix Quantities HSN-VM.B.4c

c. Understand vector subtraction vw as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

As far as subtraction goes, technically it's kind of hard to do. Remember: a vector is moving an object in a direction. How do we undo that?

Of course, we're saved by a technicality. Since subtraction is the same as adding the opposite, we'll recycle that old gem. Subtraction of vectors is just adding a vector of the appropriate length, but with the opposite direction.

When subtracting two numbers, the order matters. (Clearly, 9 minus 4 is not the same as 4 minus 9.) This is true for vectors as well and students should remember that.

Students should know that this principle of vector subtraction works the same both graphically and when applied to the components of a vector. Since adding two vectors means summing their components, subtracting two vectors means subtracting their components. It's no big mystery.