Figure 1 Coordinate system

x-component
y-component
+, if right -, if left	+, if up -, if down

Example 2: What is the sign of vector R on x-axis and on y-axis in Fig.2.9
Solution: x-component of vector R points in the positive x-direction and its magnitude must be positive. From Figure 2.9 we see that

y-component of vector R points in the positive y-direction. Its magnitude is positive. From Figure 2.9

Example 3: What is the sign of vector R on x-axis and on y-axis in Fig.2.10
Solution: x-component of vector R points in the positive x-direction. So its magnitude is positive. From Figure 2.10 we see that

y-component of vector R points in the negative y-direction. Its magnitude is negative. From Figure 2.10

Example 4: What is the sign of vector R on x-axis and on y-axis in Fig.2.11
Solution: x-component of vector R points in the negative x-direction. So its magnitude is negative. From Figure 2.11 we see that

y-component of vector R points in the negative y-direction. Its magnitude is negative. From Figure 2.11

Figure 2.12

Finding the Components of a Vector
If vector makes an angle θ with the x-axis there are two components of vector on x- axis and on y – axis (shown in Figure 2.12). As we discussed above can be expressed as the sum of two vectors: , parallel to the x-axis; and parallel to the y-axis. It was found mathematically in Eq.1 as

The projection of along the x-axis, is called the x-component of , and the projection of along the y-axis, A_y is called the y-component of . These components can be either positive or negative numbers with units. From the definitions of sine and cosine, we see that

and

So the components of are


These components form two sides of a right triangle having a hypotenuse with magnitude A. It follows that A’s magnitude and direction are related to its components through the Pythagorean theorem and the definition of the tangent:


To solve for the angle, which is measured from the positive x-axis by convention, we can write Equation 2.5 in the form

Example 5: Determine the x- and y-components of the vector A. The length of the vector A is 10.0 m. It makes an angle of 60.0° to the horizon as shown in Fig.2.13(a)

Figure 2.13(a)	Figure 2.13(b)