# 3. Vectors in 2 Dimensions

So far we have considered 1-dimensional vectors only.

Now we extend the concept to vectors in 2-dimensions. We can use the familiar x-y coordinate plane to draw our 2-dimensional vectors.

The vector V shown above is a 2-dimensional vector drawn on the x-y plane.

The vector V is acting in 2 different directions simultaneously (to the right and in the up direction). We can see that it has an x-component (6 units to the right) and a y-component (3 units up).

## Components of Vectors

Reading from the diagram above, the x-component of the vector V is 6 units.

The y-component of the vector V is 3 units.

We can write these vector components using subscripts as follows:

Vx = 6 units

Vy = 3 units

## Magnitude of a 2-dimensional Vector

The magnitude of a vector is simply the length of the vector. We can use Pythagoras' Theorem to find the length of the vector V above.

Recall (from Section 1, Vector Concepts) that we write the magnitude of V using the vertical lines notation | V |.

We have:

 Magnitude of V = | V |  = sqrt(6^2+ 3^2) = sqrt(45) = 6.71\ "units"

## Direction of a 2-dimensional Vector

To describe the direction of the vector, we normally use degrees (or radians) from the horizontal, in an anti-clockwise direction.

We use simple trigonometry to find the angle. In the above example, we know the opposite (3 units) and the adjacent (6 units) values for the angle (θ) we need.

So we have:

{: (tan\ theta,=3/6), (,=0.5) :}

This gives:

 θ = arctan 0.5 = 26.6° (= 0.464 radians)

So our vector has magnitude 6.71 units and direction 26.6° up from the right horizontal axis.

Didn't find what you are looking for on this page? Try search:

### Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Play a math game.

(Well, not really a math game, but each game was made using math...)

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

### Math Lessons on DVD

Easy to understand math lessons on DVD. See samples before you commit.