# Vector Components Worksheets

Any object that has a magnitude and a direction is considered a vector. We can visualize them by drawing a line segment with an arrow. The arrow indicates the direction, and the length of the line indicates the magnitude. We can look at vectors in a coordinate-based system and learn changes in their x and y positions. The beautiful thing about coordinate systems is that they allow us to view the vectors as angles that based on vertical and horizontal positions. If we draw a x and y axis based on the position of the vector, we can create an angle. We call these positions components of the vector. We can then evaluate the vector and the influence these components have based on vector. Over the course of these lessons and worksheets you will learn how to determine these components and learn how to identify changes in their nature.

### Aligned Standard: HSN-VM.A.2

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - Watch the angles that go across the origin.
- Quiz 2 - Remember the angles are based off of the 180 scale.
- Quiz 3 - Find the variables and just plug in from there.

### 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.

Vectors have many real-world applications because any push or pull force can be modelled with a vector. This allows us to understand everything that could possibly influence that force and either heighten or diminish the magnitude of the force. When you think of just about any form of modern transportation, it can be modelled very simply with a vector, in fact any form of motion can be modelled this way. This can allow us the ability of influence that travel in any fashion that we wish.