• N-VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
• N-VM.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
• N-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
• N-VM.4.a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
• N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
• N-VM.4.c 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 by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
• N-VM.5.a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v_x, v_y) = (cv_x, cv_y).

This award-winning web tutorial is a great choice for the crossover teacher who wants a refresher on vectors and their properties.  Included is an introduction to free-body diagrams, example problems, a series of self-paced questions, and related interactive simulations.

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