Lesson 10/20

What is the direction of the vector shown in the image?

The image isn't pointing directly up or directly to the right, but somewhere between.

To determine the exact location we need to choose a coordinate system.

The coordinated system is similar to laying a grid drawn on a piece of transparent plastic on top of a vector problem.

You choose where to put the center of the grid (the origin) and establish the direction in which the axes point.

Notice the x-axis is drawn through the origin with an arrow pointing in the positive direction.

The positive y-axis is located 90 degrees from the positive x-axis and crosses the x-axis at the origin.

Defininging a component system allows you to describe a vector in a very useful way.

Vector A in the image can now be described as going 5 units in the positive x-direction and 4 units in the positive y-direction.

You can represent this information in the form of two vectors, A_x and A_y.

Notice that A_x is parallel to the x-axis and A_y is parallel to the y-axis

If you add A_x and A_y the resultant is the original vector, A.

A vector can be broken into its components, or a vector parallel to the x-axis and another parallel to the y-axis.

A= A_x + A_y

In a two-dimensional force problem, carefully select your coordinate system.

The direction of any vector will be specified relative to those coordinates.

We define the direction of a vector as the angle that the vector makes with the x-axis.

In addition to measuring the component vector grahically, you can find the components using trigonometry.

Ax = cos ( $\theta$  )

Ay= sin ( $\theta$  )