1. Resolving Vectors in Components
Chapter 3.4B

2. Vector components
The horizontal and vertical parts that add up to give displacement are called components.
The x-component is parallel to the x-axis. The y-component is parallel to the y-axis.

3. Vector components
The components can be either positive or negative. Any vector can be completely described by a set of perpendicular components. By breaking a single vector into two components or resolving it into its components

4. Vector components
An objects motion can sometimes be described more conveniently in terms of directions such as north to south or east to west.

5. Vector components
A key to solving problems of motion is to recognize that a right angle can be drawn using velocity and its x & y components. The situation can then be analyzed using trigonometry.

6. Vector components
The sine and cosine functions are defined in terms of the length of side of such right triangle.

7. Vector components
The sine of an angle is the ration of the leg opposite that angle to the hypotenuse.
sin θ = opposite opposite hypotenuse
hypotenuse
adjacent

8. Vector components
The cosine of an angle is the ratio between the leg adjacent to the angle and the hypotenuse.
cos θ = adjacent opposite hypotenuse
hypotenuse
adjacent

9. Vector components
We have been dealing with vectors that are perpendicular to one another. In real life, many objects move in one direction and then turn at an acute angle before continuing their motion.

10. Vector components
Because the original displacement vectors do not form a right triangle, it is not possible to directly apply the tangent function or the Pythagorean theorem when adding the two original vectors.

11. Vector components
Determining the magnitude and the direction of the resultant can be achieved by resolving each of the plane’s displacement vectors into their x and y components. Then the components along each axis can be added together.

12. Vector components
c2 a2 c c1 a1 b1 b2