Standard(s):
[MA2015] PRE (9-12) 5 : 5 ) (+) 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-VM1]
[MA2015] PRE (9-12) 6 : 6 ) (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. [N-VM2]
[MA2015] PRE (9-12) 7 : 7 ) (+) Solve problems involving velocity and other quantities that can be represented by vectors. [N-VM3]
[MA2015] PRE (9-12) 8 : 8 ) (+) Add and subtract vectors. [N-VM4]
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-VM4a]
b. (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. [N-VM4b]
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-VM4c]
[MA2015] PRE (9-12) 9 : 9 ) (+) Multiply a vector by a scalar. [N-VM5]
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). [N-VM5a]
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 v (for c < 0). [N-VM5b]
[MA2015] PRE (9-12) 10 : 10 ) (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. [N-VM11]
