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### Course: Class 11 Physics (India) > Unit 8

Lesson 1: Introduction to vectors and two-dimensional motion# Introduction to two-dimensional motion: vector review

Review the key concepts and skills for two-dimensional motion, including how to add and subtract vectors.

## Key terms

Term | Meaning |
---|---|

Resultant | Sum of two or more vectors |

Vector components | Horizontal and vertical parts of a vector |

## How to add and subtract vectors

### Vector addition

To add vectors we can use the head to tail method (Figure 1).

- Place the tail of one vector at the tip of the other vector.
- Draw an arrow from the tail of the first vector to the tip of the second vector. This new vector is the sum of the first two vectors.

### Vector subtraction

Subtraction of a vector is the same as adding the vector with the opposite direction (see Figure 2).

In other words, vector $\text{-B}$ is the negative of vector $\text{B}$ if they have the same length, but point in opposite directions. Using this trick, the head to tail method of adding vectors works for subtraction as well.

## Finding perpendicular vector components

A vector can be represented as the sum of two perpendicular vector components. To find the horizontal and vertical components, we draw a right triangle with the vector as the hypotenuse $D$ (see Figure 3). One way to choose the sides of the triangle is the following:

- The
**horizontal component**( ) starts at the tail of${D}_{x}$ and is parallel to the horizontal axis. The head of the horizontal component has the same horizontal position as$D$ .$\text{D}$ - The
**vertical component**( ) starts at the head of${D}_{y}$ and ends at the head of the original vector.${D}_{x}$ is parallel to the vertical axis.${D}_{y}$

## Common mistakes and misconceptions

**A common mistake is attempting to add vectors head to head, or tail to tail.**However, this approach is incorrect, and gives a different answer from adding the vectors head to tail (Figure 4).

**Some people think vectors have to be added in a particular order.**Since vector math is commutative, the order does not matter.

## Learn more

To check your understanding and work toward mastering these concepts, check out the exercise on describing two-dimensional motion with vectors.

## Want to join the conversation?

- Why is this in science?(0 votes)
- This is in the AP Physics 1 class. Physics is a type of science.(26 votes)

- why does "head to head" or "tail to tail" not work?(7 votes)
- What is the condition for two vectors A+B to be equal to A-B?(5 votes)
- Can we add up three vectors at once like this too(4 votes)
- why is the vectors the sums of the two vectors even tho theyre not perfectly aligned.(2 votes)
- how many lesson are there or parts ?(2 votes)
- what is the difference between figure 4 two triangles?(2 votes)
- im lost beyond recognition, one vectors sum is equal to 2 different vectors? can someone explain pls(1 vote)
- Lets think of a vector as a line. Lets say its drawn on your paper at about a 45-degree angle. That would look similar to his: /

Now, the idea that two vectors can equal another vector can be visualized if you can draw two different lines starting at one point of the line and ending at the other. That's all it is. In physics, we use two perpendicular lines, one going in the x direction (left and right) and the other line going in the y direction (up and down).(2 votes)

- why is there an exercise, but no video? how am I supposed to know what I'm doing if there is no instructional video?(0 votes)
- Because it's like the most straightforward idea in physics.(3 votes)

- How do you add two 2D vectors in python?(1 vote)