1. Vectors
What is a vector?

2. What is a vector?
In science measurements of various quantities can be categorized into two main groups Scalar and Vector.
Quantities that have only magnitude (size) are called Scalars.
Quantities that have both magnitude AND direction are called Vectors.
Magnitude – a number, quantity, how much, size

3. Scalar Vector Distance – how far Speed – how fast
Displacement – how far with a direction
Velocity – how fast with a direction
Acceleration – speeding up/slowing down with a direction

4. Scalar Vector Mass – the amount of matter in an object Time – how long
Volume – the amount of space an object takes up
Work – Force acting through a displacement
Weight – the force of gravity acting on an object
Force – a push or pull
Torque – force of rotation
Magnetic Field Strength

5. How to represent a vector?
All vectors in science are represented by Arrows
The size represents the magnitude
The arrow represents the direction of the vector
Negatives mean opposite direction

6. Adding/Subtracting (adding a negative)
When vectors are 0 and 180 degrees in difference
You add vectors just like you would numbers, but you must take their direction into account
Ex: S + 10 S = 15 S

7. Drawing Method
When visually representing vectors you must make sure you follow the “Tip to Tail” method.
Draw your first vector then draw the next vector at the tip of last one. Then solve it mathematically.
The answer is called the resultant vector (VR).
tail
tip
Vector

8. Drawing Method Now you try! 3.0 West + 4.0 West =
4.0 North South =
6.0 North – 3.0 South =
HW: Diagram Skills front and Vector Addition 1-6

9. Adding to vectors that are 90 degree difference
Before we start this procedure we must first review our trigonometric functions. Remember SOH CAH TOA 
θ =

10. Adding Vectors with 90 cont’d
First DRAW your vector addition using the “Tip to Tail” method
Then use the Pythagorean Theorem and the Inverse Tangent function to solve mathematically.
Ex: Add 10.0 m/s E to 15.0 N
Step 2 (Pythagorean) Step 3 (Tan-1)
HW: Vector Addition Practice 1-10

11. Now let’s try and do the oppostie!
If I give you a vector at an angle and ask for the x and y components of the vector, that means I’m giving you the resultant and asking for the vectors that make it up.
Ex: What are the components of 25 m, 65° NE?
HW: Vector Addition Practice 11-15

12. Adding With Multiple Vector Types
There are five steps:
Draw a picture
Resolve any vectors at an angle into their x and y components
Find your x sum and y sum by combining all the x’s and all the y’s
Draw the new picture using your x sum and y sum
Use the Pythagorean Theorem and the tangent function to solve

13. Let’s Try One! 16.0 m East + 20.0 m, 35.0° SE
HW: Vector Addition Practice 16-20

14. Divide/Multiply a Vector by a Scalar
The rule here is just divide/multiply the magnitude and keep the direction the same.
Make sure you keep your sig. fig. rules
Example:
10.0 m S / 4.0 = 2.5 m
3.0 m E x 4.0 m = 12 m E

15. Multiply a Vector by a Another Vector
There are 2 types of vector multiplication.
DOT PRODUCT
In this calculation when you multiple the vectors you get a SCALAR for the answer.
CROSS PRODUCT
In this calculation when you multiple the vectors you get a vector as the result. However, you have to use the right hand rule to find the resulting direction.