Vectors

1. Vectors What is a vector?

2. Basics • There are two types of values used everyday in the world to describe movement and quantity. • Scalars and Vectors • These are used to describe the various conditions, quantities and motion seen everywhere in the world.

3. Scalars • A value that states a quantity, size or magnitude. • Only gives a size to a value. • Commonly used for prices, length, height, width, volume, mass, # of product • Ex: • $10.00 , 20 m , 2 x 4 , 10:00 PM • 120 min. , 1340 ft. , 13 mi. , 55 mph • All are scalars, size values only

4. Vectors • What is a vector? • Slightly more complicated than a scalar. • Has both a magnitude and a direction. • EX: • 20 m North , 4 steps to the left, 65 mph North

5. Distance = scalar Speed = scalar Velocity = vector Acceleration = vector Position = scalar Price = scalar Height = scalar Force = vector Heat = scalar Mass = scalar Weight = vector Distance traveled = scalar Displacement = vector Scalar or Vector?

6. How are they written? • Scalars are written as regular variables. • You have been doing it this way for years. • Vectors, now they are different, because they have more information. • Any vector variable in an equation will have an arrow above it showing it as a vector. • also be shown in bold type in a text book. d d

7. Graphical representation • Scalars – represented by a number. • Vectors – represented by directional arrow. • Length of the arrow is the magnitude of the vector. • Direction of the arrow is what makes the value a vector Angle or direction

8. Parts of a vector Tip • Tail – starting point of the vector • Tip – arrow and ending point of the vector • Length is the magnitude. • Angle – direction the vector is pointing Angle or direction Tail

9. How it works? • A drawn vector represents the value of the vector by it’s length. • IF the vector is moved, it must maintain the same direction or orientation

10. Equality A • Equivalent or equal vectors are vectors that have both the same magnitude and orientation. • Any difference in either means they are not equivalent or equal. B D C A = B , But A does not equal C or D.

11. Adding - Graphically • Vectors are added using graphical position. • Each vector being added is placed in order from first to last. • Their resultant or sum is a vector that goes from the starting point to the ending point. A B D C D is the resultant or sum of the vectors

12. Adding - Graphically • There is a method to the addition. 1. The orientation of each vector can not be changed. 2. They are to be added in order. Tail of the second vector in the sum is placed at the tip of the one before it. This continues until there are no more vectors to be added. 3. The result is drawn and then measured from the tail of the very first vector to the tip of the very last vector in the series.

13. C B A Adding • Tail of B is placed on the tip of A. • The resultant is drawn from the tail of A to the tip of B. • Vector C is the sum of vectors A and B.

14. A B C Adding • Tail of B is placed on the tip of A. • Vector C is the sum of vectors A and B.