1. Vectors: Resolution and Addition

2. Vectors: The Basics Vector: has both magnitude and direction
Examples: displacement, velocity, acceleration
Scalar: has magnitude but no direction
Examples: distance, speed, time, mass
Drawing Vectors
represented by arrows
length represents magnitude
angle and head of arrow shows direction (angle)
labeled with quantity and/or value
v1 = 3 m/s
30

3. Vector Components
Some vectors point directly along x or y axes, but most do not.
Components
how much in x & y directions
components are still vectors  have direction
2 component vectors represent original vector
Henderson, Tom (n.d.) Vector Components. The Physics Classroom. Retrieved from

4. Vector Resolution: Graphical Method
Sketch projection lines to x & y axis
Draw component vectors along axes
Hepburn, Carl Jason. (n.d.) Scalars and Vectors. Splung.com. Retrieved from

5. Vector Resolution: Algebraic Method
Visualize vector and its components as a right triangle.
Use SOH CAH TOA to calculate components
Fullerton, Daniel B. (n.d.) Regents Physics Math Review. APlusPhysics.com. Retrieved from

6. Vector Resolution: An Example
You might want to click here for a video review of trigonometry and listen to this song about SOH CAH TOA. If you feel comfortable with trigonometry, just click on the link below. If the links do not work, copy & paste into your browser.
Watch this video demonstration of vector resolution done graphically and algebraically.
Khan, Salman. (n.d.) Basic Trigonometry. Video posted to
KDogde314. (2010, March 25). SOH CAH TOA Song. Video posted to
dejongescience. (2010, July 11). Basic vector resolution. Video posted to

7. Vector Addition
Add vectors to find the net (overall) magnitude and quantity of what is being measured (i.e. displacement, velocity, force).
Resultant: the one vector that represents the sum of two or more vectors
Only vectors of the same quantity and units may be added or subtracted
You can’t add a velocity vector and a displacement vector
You can’t add a velocity in m/s with a velocity in mph

8. Vector Addition: Graphical Method
Draw 1st vector
Begin tail of 2nd vector at head of 1st vector
Begin tail of 3rd vector at head of 2nd vector
Continue until there are no more vectors
Draw resultant vector from tail of 1st vector to head of last vector. Label resultant.
Appendix: Simple Vectors for Preliminary High School Physics. (2007, April 26) Retrieved from the Bored of Studies wiki:

9. Vectors Can Be Added In Any Order
Vectors can be moved parallel to themselves in a diagram.
Vectors can be added in any order.
Resultant will always be the same.
Henderson, Tom (n.d.) Vector Addition: The Order Does NOT Matter. The Physics Classroom. Retrieved from

10. Resultant of Collinear Vectors
Same direction: add
Opposite directions: subtract

11. Resultant of Perpendicular Vectors
What is the turtle’s resultant displacement from Po to Pf?
Vectors: sides of a right triangle
Resultant: hypotenuse
How to solve?: Pythagorean theorem
Inverse tangent to find angle
Resultant:  N of E

12. Vector Addition: Examples
Let’s make sure you get it. Watch this video demonstration of the addition of 2 perpendicular vectors.
But, wait!!! What do we do when our vectors are not perpendicular or there are 3 or more vectors?
Watch this video demonstration to find out!
dejongescience. (2010, July 11). Vector addition at right angles. Video posted to
PhunScience. (2011, August 1). Adding Vectors: How to Find the Resultant of Three or More Vectors. Video posted to

13. Summary: Vector Addition of Non-Perpendicular Vectors (or 3 or more vectors)
Use the “vector components” method by first resolving all vectors into their components.
Magnitude:
Find the sum of all x-components and all y-components.
These are the component s of the resultant vector.
Use Pythagorean Theorem to find resultant from components.
Use Inverse tangent to find precise direction of resultant.