## Finding the Components of a Vector

#### Aligned To Common Core Standard:

**High School** - HSN-VM.A.2

What Are the Components of a Vector?
During the discussion of vectors, we come across many vectors that act together and can be combined together to give a single vector. Similarly, a vector can be broken down into its components to which, when combined/added together, will yield the same original vector. The vectors which are broken down are known as the components of the original vector. The entire process of breaking down a vector into its many separate components is called resolving a vector into components.
A vector can be broken into x -component and y -component in a two-dimensional coordinate system like; V= (v_{x} , v_{y})
The components of a vector can be quickly and easily identified. The most useful is to resolve which is at the right angles to the other vector, usually horizontal and vertical. The vectors parallel to the two-dimensional coordinate system of x and y axes are straightforward problems to solve. It makes easy for us to use the trigonometric identities to ascertain the magnitude of the components of the vector.

### Printable Worksheets And Lessons

- Finding x and y of a Vector Step-by-step Lesson- Very similar to converting polar coordinates to rectangular form.

- Guided Lesson - These vectors are draw for you and you need to convert the position statements to x,y form.

- Guided Lesson Explanation - All three problems use the same formula. We get you headed in that direction and magnitude; pun intended.

- Practice Worksheet - Ten problems spread over two pages.

- Matching Worksheet - Match the drawn vectors to the rectangular form of their coordinates.

#### Homework Sheets

Find the x and y parts of the vector. This will prep students for the next phase of vectors.

- Homework 1 - You can find the x and y coordinates using the following formulas: x = r cos Θ and y = r sin Θ
- Homework 2 - Read the magnitudes properly before you get going here.
- Homework 3 - The angles are written bigger here.

#### Practice Worksheets

This is a fundamental skill that students have to master before proceeding to the next level.

- Practice 1 - Start by establishing what each variable stands for.
- Practice 2 - Find the x and y components of the following vector.
- Practice 3 - Plug the values into the formulas for finding the coordinates.

#### Math Skill Quizzes

I often find that students that struggle with vectors never truly took the time to get this skill.