In these lessons, we will learn about equal vectors and solve simple problems involving equality of vectors.

**Related Pages**

Vectors

Vector Addition

Vector Subtraction

Vector Multiplication

Vector Geometry

**What are equal vectors?**

Equal vectors are vectors that have the same magnitude and the same direction.

Equal vectors may start at different positions. Note that when the vectors are equal, the directed line segments are parallel.

**Equality Of Column Vectors** If two vectors are equal then their vector columns are equal.

**Example:**

The column vectors **p** and **q** are defined by

Given that **p** = **q**

a) find the values of x and y

b) find the values of and

c) express y in terms of x

**Solution:**

**Equal vectors and negative vectors**

**Magnitude of Vectors and Equal Vectors**

When are two vectors equal?

Two vectors are equal if they have the same length (magnitude) and direction.

**Example:**

- Let u be the vector represented by the directed line segment from R = (-4, 2) to S = (-1, 6)

a) Find the magnitude of u.

b) Find the component form of the vector.

**Equal Vectors**

What are the conditions necessary for vectors to be considered equal?

Two vectors are equal if they have the same length and direction and are parallel.

What is a negative vector?

**Equivalent vectors examples**

**Example:**

Are vectors u and w equivalent?

Yes, they are equivalent.

No, they have the same magnitude, but different directions.

No, they have the same direction, but different magnitudes.

No, they have different magnitudes and directions.

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