### Topics

- Vectors
- Vector Components
- Vector Addition
- Equations

- Vectors
- Vector Components
- Vector Addition
- Equations

- Describe a vector in your own words
- Explain a method to add vectors
- Compare and contrast the component styles
- Decompose a vector into components
- Describe what happens to a vector when it is multiplied by a scalar
- Arrange vectors graphically to represent vector addition or subtraction

HSN-VM.B.5b

Compute the magnitude of a scalar multiple*c*using ||*v**c*|| = |*v**c*|. Compute the direction of*v**c*knowing that when |*v**c*|≠ 0, the direction of*v**c*is either along*v*(for*v**c*> 0) or against(for*v**c*< 0).HSN-VM.B.5a

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}).HSN-VM.B.5

(+) Multiply a vector by a scalar.HSN-VM.B.4c

Understand vector subtraction-*v*as*w*+ (-*v*), 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.*w*HSN-VM.B.4b

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.HSN-VM.B.4a

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.HSN-VM.B.4

(+) Add and subtract vectors.HSN-VM.A.2

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.HSN-VM.A.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*).

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