# ALEX Classroom Resource

## Precalculus and Advanced Topics Module 2, Topic D: Vectors in Plane and Space

Classroom Resource Information

Title:

Precalculus and Advanced Topics Module 2, Topic D: Vectors in Plane and Space

URL:

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 2, Topic D opens with a formal definition of a vector. The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical frameworks for these operations. Students solve problems involving velocity and other quantities that can be represented by vectors. Parametric equations are introduced allowing students to connect their prior work with functions to vectors.

Content Standard(s):
 Mathematics MA2015 (2016) Grade: 9-12 Precalculus 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] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 6 ) (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. [N-VM2] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 7 ) (+) Solve problems involving velocity and other quantities that can be represented by vectors. [N-VM3] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 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] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 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] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 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]
Tags: add, coordinates, line segments, magnitude, matrix, multiply, scalar, subtract, transformations, vector, velocity