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Scalar multiplication of vectors

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Discrete Mathematics/Computer Science
30. CC.HSN.VM.A.2
30.2 Scalar multiplication of vectors

Scalar Multiplication of Vectors

Discover how multiplying a vector by a scalar stretches, shrinks, or flips it, and practice the component formula with step-by-step examples.

What You'll Learn

Multiply each component of a vector by the scalar to find the scalar multiple.
Calculate how a scalar changes a vector's magnitude by taking the absolute value of the scalar times the original magnitude.
Recognize that a negative scalar reverses the vector's direction while a positive scalar keeps it the same.
Apply the distributive and associative properties to simplify expressions with scalars and vectors.
Identify when a scalar multiple produces an equivalent or parallel vector.
Combine scalar multiplication with vector addition to solve linear combination problems.

What You'll Practice

1

Multiplying vectors in component form by positive and negative scalars

2

Finding magnitudes of scaled vectors

3

Factoring scalars from vector expressions

4

Working with fractional scalar multipliers

Why This Matters

Scalar multiplication is essential for physics applications like calculating velocity, force, and displacement. You'll use this skill throughout calculus, engineering, and any field involving motion, direction, and magnitude relationships.

Before You Start — Make Sure You Can:

Reflection across the x-axis: y = -f(x)Transformations of functions: Horizontal stretchesTransformations of functions: Vertical stretches

This Unit Includes

7 Video lessons
Practice exercises
Learning resources

Skills

Scalar Multiplication
Vectors
Magnitude
Component Form
Distributive Property
Vector Operations
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