In these lessons, we will learn how to subtract vectors by adding its negative, how to subtract vectors geometrically using the head-to-tail method and how to subtract vectors using their components.

Related Topics:

Vector Addition

More lessons on Vectors

**What is a vector?**

A vector is a quantity that has magnitude (size) and direction.

**How to represent a vector graphically, in column-vector form and in unit-vector form?**
### How to subtract Vectors?

Subtracting a vector is the same as adding its negative.

The difference of the vectors**p** and **q** is the sum of **p** and –**q**.

**p** – **q** = **p + **(–**q**)
**How to subtract vectors using column vectors and explained graphically?**

**How to subtract vectors graphically?**
**Geometric subtraction of two vectors**
**How to solve word problems using vector subtraction?**
**Vector word problems when given magnitude and direction**

Subtract the following vectors (B - A)

A = 5.0 m at 40 degrees west of North

B = 2.5 m south.

Find the distance and direction of (B - A)**Vector subtraction including boat example**

Introduction to 'head to tail' vector subtraction in the geometric sense. This is then applied to an example of working out a boat's velocity relative to water given the velocity of the current and the velocity of the boat relative to land are both known.

velocity relative to land = water velocity + boat's velocity relative to water

Example:

A woman wants to get to a destination that is due North of her starting point. To do this, she needs to row across a stream. The current is flowing East at 12km/hr. The woman can row the boat at a constant speed of 16km/hr.

What will be the required direction that she must row the boat in order to reach the required destination?

### How to subtract vectors using their components

Subtracting Vectors in Component Form for 2-D and 3-D vectors.
**How to add and subtract vectors in component form?**

Example:

Let u = <-1, 3>, v = <2, 4>, and w = <2, -5>. Find the component form of the vector

u + v

u - w

2u + 3w

2u - 4v

-2u - 3v

Related Topics:

Vector Addition

More lessons on Vectors

A vector is a quantity that has magnitude (size) and direction.

The difference of the vectors

** Example: **

Subtract the vector **v** from the vector **u**.

** Solution: **

** u ** – **v** = **u** + (–**v**)

Change the direction of vector **v** to get the vector –**v**.

**Check:** The column vector should represent the vector that was drawn.

**How to subtract vectors using column vectors?**

u - v = u + (-v)

Since we know how to add vectors and multiply by negative one, we can also subtract vectors.

Subtract the following vectors (B - A)

A = 5.0 m at 40 degrees west of North

B = 2.5 m south.

Find the distance and direction of (B - A)

Introduction to 'head to tail' vector subtraction in the geometric sense. This is then applied to an example of working out a boat's velocity relative to water given the velocity of the current and the velocity of the boat relative to land are both known.

velocity relative to land = water velocity + boat's velocity relative to water

Example:

A woman wants to get to a destination that is due North of her starting point. To do this, she needs to row across a stream. The current is flowing East at 12km/hr. The woman can row the boat at a constant speed of 16km/hr.

What will be the required direction that she must row the boat in order to reach the required destination?

Example:

Let u = <-1, 3>, v = <2, 4>, and w = <2, -5>. Find the component form of the vector

u + v

u - w

2u + 3w

2u - 4v

-2u - 3v

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