Related Topics:

Vectors, Scalar Multiplication of Vectors

**Multiplying a vector by a scalar**

**Multiplying a Vector by a Scalar**

How to multiply a vector by a scalar including some algebraic properties of scalar multiplication.

Discuss the concept of a linear combination of vectors and shows an example of drawing a geometric sum/difference of 3 vectors.

Multiplying a vector by a scalar (real number) means taking a multiple of a vector.

Two vectors are said to be collinear when they are drawn tail to tail and they lie on the same line.

If a and b are two non-collinear vectors in the plane, then any other vector can be written as a linear combination of a and b.

Properties of Scalar Multiplication

Let v be any vector and k be a scalar. Then kv is a vector and kv is |k| times as long as v.

• If k > 0, kv has the same direction as v.

• If k < 0, kv has the opposite direction as v.

• If k = 0, kv is the zero vector.

Examples:

1. Given the vector 75 km/h [N 50° E] draw twice this vector.

2. OF = 3b and OE = 2a, write each of the following in terms of a and b.

a) EF

b) OG

**How to show geometrically what multiplication of a vector by a scalar is?**

**Understanding multiplying vectors by scalars**

Examples:

w = (1,2)

Find 3w

Find -2w

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Vectors, Scalar Multiplication of Vectors

A scalar quantity has a magnitude but no direction.

In vectors, a fixed numeric value is called a scalar.

A vector can be multiplied by a **scalar**.

When a vector **x** is multiplied by 3, the result is 3**x**.

When a vector **x** is multiplied by –2, the result is –2**x**.

In the above examples, 3 and –2 are scalars.

How to multiply a vector by a scalar including some algebraic properties of scalar multiplication.

Discuss the concept of a linear combination of vectors and shows an example of drawing a geometric sum/difference of 3 vectors.

Multiplying a vector by a scalar (real number) means taking a multiple of a vector.

Two vectors are said to be collinear when they are drawn tail to tail and they lie on the same line.

If a and b are two non-collinear vectors in the plane, then any other vector can be written as a linear combination of a and b.

Properties of Scalar Multiplication

Let v be any vector and k be a scalar. Then kv is a vector and kv is |k| times as long as v.

• If k > 0, kv has the same direction as v.

• If k < 0, kv has the opposite direction as v.

• If k = 0, kv is the zero vector.

Examples:

1. Given the vector 75 km/h [N 50° E] draw twice this vector.

2. OF = 3b and OE = 2a, write each of the following in terms of a and b.

a) EF

b) OG

Examples:

w = (1,2)

Find 3w

Find -2w

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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