Common Core · High school
HSN-VM.B.4.C
High school — Understand vector subtraction v − w 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 and perform it component-wise.
A note on this mapping: HSN-VM.B.4.C is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The skill that covers it
What a student should be able to do
- Write the component form of a vector between two points, and find its magnitude.
- Find the direction angle of a vector, and the components of a vector from its magnitude and direction.
- Add and subtract vectors, multiply by a scalar, and simplify a linear combination such as 3u - 2v.
- Find a unit vector in the direction of a given vector, and convert between component and i, j notation.