# Vector Addition Worksheets

Vectors are really accurate approximations of values with direction. They are often used to model motion of all types. From you walking down your street to pickup a gallon of milk to an astronaut blasting off in a rocket. There are many times when we need to model all of the forces that surround the motion of something. Such as a car moving on a road. The force of gravity exerts a resulting vector of drag of friction on the car. So, while the car can have a vector of its own to describe the motion another vector can be drawn to describe the frictional forces that are exerted on the car. You can then determine the overall net force by adding those two vectors together. This worksheet series shows students how to use vector addition to find the end result of two vectors which in motion is usually a measure of net force.

### Aligned Standard: HSN-VM.B.4b

- Vector Sums Step-by-step Lesson- The method I use here is sometimes called Triangle Vector Addition.
- Guided Lesson - Find the sum of the three different sets of vectors.
- Guided Lesson Explanation - I used different colors to delineate between the two vectors. It would help to print this one in color.
- Practice Worksheet - Four pages of vectors to start adding up.
- Matching Worksheet - Match the vector to the sum that they generate.

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

### Homework Sheets

This skill is often studying early on in physics.

- Homework 1 - Count the number of blocks covered by two vectors.
- Homework 2 - The vectors are plotted and the resultant is the hypotenuse.
- Homework 3 - This is a useful strategy to visually respresent the movement of an object.

### Practice Worksheets

This is sometimes referred to as Impact Science. You can use this skill to estimate or calculate levels of damage in car accidents.

- Practice 1 - Find the sum of each pair of vectors (the magnitude of the resultant vector).
- Practice 2 - To find the resultant vector's magnitude, use the Pythagorean Theorem.
- Practice 3 - The resultant is: x
^{2}+ y^{2}= r^{2}

### Math Skill Quizzes

The graphs are purposely not labeled. Expect to see this on tests as well.

- Quiz 1 - The answers are found as the last page.
- Quiz 2 - Make sure there is enough space to work with here.
- Quiz 3 - The applications to physics here are tight.

### How to Add Vectors End to End

Adding vectors can sometimes be a complicated procedure. Here are a few procedures with steps that can help you add your vectors from end to end.

**Explanation #1** - The first step that is involved you have to find the sum of each of the vectors. Second step includes drawing the lines that indicate and model the vectors. Step three involves counting the blocks that have been covered by the two vectors: x = 3 y = 4

Step four involves finding magnitude of the the resultant vector. For this step the most common approach is using the Pythagoras Theorem which is: a^{2} + b^{2} = c^{2}

The resultant vectors in this case will be: x^{2} + y^{2} = r^{2} or 32 + 42 = r^{2} | r = √ (32 + 42) | r = 5

**Explanation #2** - The first step involves understanding what is being asked in the question which is usually going to be "find the sum of the vectors". The second step is to draw those legs again and see where they fall. Step three involves the same step as previous one, counting the number of blocks covered by each vector: x = 5, y = 5

The fourth step is finding the resultant factor using the Pythagorean theorem: a^{2} + b^{2} = c^{2}. The resultant vector is: 52 + 52 = r^{2} | The resultant is r = √ (52 + 52) | r = 7.07.