Common Core · High school
HSN-VM.A.1
High school — Recognise vector quantities as having both magnitude and direction; represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
A note on this mapping: HSN-VM.A.1 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The 2 skills that cover it
- VectorsA quantity with a size and a direction: write a vector in component form, find its magnitude and direction angle, add, subtract and scale vectors, build one from a magnitude and an angle, and find the unit vector that points the same way.Read the lesson →
- Vectors in n DimensionsA vector stops being an arrow on a page and becomes a list of numbers of any length: add and scale vectors in three, four or n dimensions, measure their length, find the unit vector along one, take a dot product to test whether two are perpendicular, and write a line in space as a point plus a direction.Read the lesson →
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.
- Add, subtract and scale vectors in three or more dimensions, component by component.
- Find the magnitude of a vector in n dimensions, the distance between two points, and the unit vector in a given direction.
- Compute the dot product in n dimensions, decide whether two vectors are orthogonal, and find the value that makes them so.
- Write the vector equation of a line in space and find the point at a given parameter.