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Common Core (Vector and Matrix Quantities)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to 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}).

### Suggested Learning Targets

The following diagram shows how to multiply a vector by a scalar. Scroll down the page for more examples and solutions of scalar multiplication.

**Multiplying a Vector by a Scalar**

This video shows how to multiply a vector by a scalar including some algebraic properties of scalar multiplication. The lesson also discusses briefly the concept of a linear combination of vectors and shows an example of drawing a geometric sum/difference of 3 vectors.

**Vector Addition and Scalar Multiplication, Example 1**

In this video, we look at vector addition and scalar multiplication algebraically using the component form of the vector.
**Vector Addition and Scalar Multiplication, Example 2**

In this video we add two vectors in component form and also sketch the vectors to illustrate how to add vectors graphically.**Vectors, Addition, Subtraction and Scalar Multiplication**
**Multiplying a Vector by a Scalar**

This lesson presents the properties of multiplication of a vector by a scalar. You will also learn what collinear vectors represent and how to verify that two vectors are collinear or parallel.

Common Core (Vector and Matrix Quantities)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as

- I can multiply a vector by a scalar graphically.
- I can multiply a vector by a scalar component-wise.

The following diagram shows how to multiply a vector by a scalar. Scroll down the page for more examples and solutions of scalar multiplication.

This video shows how to multiply a vector by a scalar including some algebraic properties of scalar multiplication. The lesson also discusses briefly the concept of a linear combination of vectors and shows an example of drawing a geometric sum/difference of 3 vectors.

In this video, we look at vector addition and scalar multiplication algebraically using the component form of the vector.

In this video we add two vectors in component form and also sketch the vectors to illustrate how to add vectors graphically.

This lesson presents the properties of multiplication of a vector by a scalar. You will also learn what collinear vectors represent and how to verify that two vectors are collinear or parallel.

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