Vector components

In this lesson, we will learn:

Notes:

Components of a vector are other vectors that add up tip-to-tail give you the original vector.
- The x and y components of a vector are the components that are pointed directly in the x and y directions, respectively, and are useful for solving problems.
- The x and y components can be found with trigonometry, since they always form a right triangle with the original vector.

Right Triangle Trigonometric Equations

$\sin(\theta) = \frac{opp.}{hyp.}$

$\cos(\theta) = \frac{adj.}{hyp.}$

$\tan(\theta) = \frac{opp.}{adj.}$

$a^{2}+b^{2}=c^{2}$ (Pythagorean theorem)

$\theta$ : angle, in degrees (°)

$opp.$ : side opposite angle

$adj.$ : side adjacent angle

$hyp.$ : hypotenuse of triangle (longest side, side opposite 90° angle)

$a$ and $b$ : non-hypotenuse sides of triangle

$c$ : hypotenuse of triangle

Introduction
Introduction to vector components:
- What are x and y components?
- How to break a vector into its components

1.
Break a displacement into vector components
A boat sails 33.0 km at 55.0° north of west. What are the north and west components of its displacement?

3.
Add two 2D vectors using components
Solve the equation $\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res}$ by breaking $\vec{v}_{1}$ and $\vec{v}_{2}$ into their x and y components.