**Vector Characteristics**

Vector Components

Vector Components Cont'd Some Mo

Earlier we resolved vectors into x & y components based on the angle and magnitude of the resultant vector.

**Vector Components Cont'd**

The way that we find those x & y components of vectors is by using basic trigonometry functions.

**4.1 & 4.2 Vectors in Physics/Adding & Subtracting Vectors**

What sets vectors apart from scalars in physics is that vectors have both

magnitude

and direction.

Vectors are Represented by an arrow.

(refers to the length of the vector)

Vectors have length and direction.

In the text, vectors are represented by

boldface

lettering and a small arrow above the letter. Like the

r

listed in the diagram to the left.

The magnitude of this vector would be symbolized by

italics

of the same letter.

For example, the magnitude of

r

is

r

= 1.0 km

When handwriting a vector symbol, we write the letter for the vector with an arrow over it as well.

How do we represent vectors?

Since we can't just walk in a straight line to get to the library, you would have to walk west and north along the streets.

Walking this way, we

resolve

the displacement vector

r

into east-west and north-south

components

.

To resolve a vector means to find its components; a vector's components are the lengths of the vector along the x and/or y directions.

Recall that sine and cosine of an angle theta is defined in terms of a right triangle.

The cosine of an angle theta is the length of the adjacent side divided by the length of the hypotenuse.

sine of an angle theta is the length of the opposite side divided by the length of the hypotenuse.

this is how you see it in math...

this is how we rearrange it and apply it to physics...

make sure your calculator is in degree mode, NOT radians!!!

see page 117 for examples

Individual vectors can be treated like vector components to find the resultant vector and its direction.

The magnitude of the resultant vector can be found by using the Pythagorean Theorem.

a + b = c

2 2 2

c

a

b

To find the angle of the resultant vector, we use the tangent function and rearrange it to solve for the angle theta.

see page 119 for examples

Adding & Subtracting Vectors

Earlier, we discussed vector addition and how we place vectors head to tail.

The

resultant

vector (vector sum) is the result of adding two or more vectors.

Vector Addition Rule #1:

To add two vectors A and B, place the tail end of B at the head of A.

The sum C = A + B is the vector that extends from the tail of A to the head of B.

A

B

C

A +

B

C =

What if the things are a little more involved...

Vector Addition Rule #2:

When adding two or more vectors, first place all of the vectors head to tail, then draw the resultant vector from the

tail

of the

first

vector to the

head

of the

last

vector.

Subtracting vectors is a little different