Common Core · High school
HSN-VM.B.5.B
High school — Compute the magnitude of a scalar multiple cv using ||cv|| = |c| v; compute the direction of cv knowing that when |c| v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
A note on this mapping: HSN-VM.B.5.B 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.