# Equal Vectors

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

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:

1. 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.

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