# 5.15: Vector Subtraction

**At Grade**Created by: CK-12

**Practice**Vector Subtraction

You and a friend are trying to position a heavy sculpture out in front of your school. Fortunately, the sculpture is on rollers, so you can move it around easily and slide it into place. While you are applying force to the sculpture, it starts to move. The vectors you and your friend are applying look like this:

However, the sculpture starts to move too far and overshoots where it is supposed to be. You quickly tell your friend to pull instead of push, in effect subtracting her force vector, where before it was being added. Can you represent this graphically?

By the end of this Concept, you'll know how to represent the subtraction of vectors and answer this question.

### Watch This

### Guidance

As you know from Algebra, **negative** vector is the same magnitude of the original vector, but its direction is opposite.

In order to subtract two vectors, we can use either the triangle method or the parallelogram method from above. The only difference is that instead of adding vectors

#### Example A

Using the triangle method for subtraction.

#### Example B

#### Example C

### Guided Practice

1. For the vector subtraction below, make a diagram of the subtraction.

2. For the vector subtraction below, make a diagram of the subtraction.

3. For the vector subtraction below, make a diagram of the subtraction.

**Solutions:**

1.

2.

3.

### Concept Problem Solution

As you've seen in this Concept, subtracting a vector is the same as adding the negative of the original vector. This is exactly like the rule for adding a negative number to a positive number. Therefore, to change your friend's force vector to a subtraction instead of an addition, you need to change the direction by

### Explore More

- Find the coordinates of the terminal point of
a⃗−b⃗ . - What is the magnitude of
a⃗−b⃗ ? - What is the direction of
a⃗−b⃗ ?

- Find the coordinates of the terminal point of
c⃗−d⃗ . - What is the magnitude of
c⃗−d⃗ ? - What is the direction of
c⃗−d⃗ ?

- Find the coordinates of the terminal point of
e⃗−f⃗ . - What is the magnitude of
e⃗−f⃗ ? - What is the direction of
e⃗−f⃗ ?

- Find the coordinates of the terminal point of
g⃗−h⃗ . - What is the magnitude of
g⃗−h⃗ ? - What is the direction of
g⃗−h⃗ ?

- Find the coordinates of the terminal point of
i⃗−j⃗ . - What is the magnitude of
i⃗−j⃗ ? - What is the direction of
i⃗−j⃗ ?

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 5.15.

Negative Vector

A negative vector is a vector that is the same magnitude as the original vector, but the opposite direction.Triangle Method

The triangle method is a method of adding vectors by connecting the tail of one vector to the head of another vector.### Image Attributions

## Description

## Learning Objectives

Here you'll learn how to subtract two vectors using the triangle method.

## Difficulty Level:

At Grade## Authors:

## Subjects:

## Search Keywords:

## Concept Nodes:

## Date Created:

Sep 26, 2012## Last Modified:

Feb 26, 2015## Vocabulary

**Save or share your relevant files like activites, homework and worksheet.**

To add resources, you must be the owner of the Modality. Click Customize to make your own copy.