### N: Number and Quantity

#### N.VM: Vector and Matrix Quantities

(Framing Text): Represent and model with vector quantities.

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).

Adding Vectors

Vectors

N.VM.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Vectors

N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions

Golf Range

(Framing Text): Perform operations on vectors.

N.VM.4: Add and subtract 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.

Adding Vectors

Vectors

N.VM.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

Adding Vectors

Vectors

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.

Adding Vectors

Vectors

N.VM.5: Multiply a vector by a scalar.

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(vx , vy) = (cvx , cvy).

Dilations

Vectors

N.VM.5.b: 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 vs (for c < 0).

Vectors

(Framing Text): Perform operations on matrices and use matrices in applications.

N.VM.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the pay-offs in a game are doubled.

Dilations

Correlation last revised: 9/16/2020