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

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