Vectors

There are two kinds of quantities… Vectors have both magnitude and direction Scalars have magnitude only What is magnitude? Size or Amount

How you will see magnitude: Timmy pushes a chair 3 feet forward and 2 feet backward. What is the magnitude of the chair’s displacement? What is magnitude? You are solving for displacement, not magnitude Magnitude means the number & units only

Drawing Vectors Vectors are drawn as Arrows  head tail

Direction of Vectors A B The arrow head shows the direction of the vector B

Magnitude of Vectors A B The magnitude of the vector is represented by the length of the arrow B

Magnitude of Vectors A 2A If vector A represents a displacement of three miles to the north… 2A Then vector 2A, (which means 2 x A) is twice as long, and would represent a displacement of six miles to the north!

Opposite Vectors Opposite vectors have the same length, but opposite direction. A -A

Graphical Addition of Vectors: Head to Tail B A R A + B = R R is called the resultant vector!

Graphical Addition of Vectors: Head to Tail -B A - B = R R A A + (-B) = R R is called the resultant vector!

Vectors: Components Horizontal (x-components) and vertical (y-components) must be added separately to determine the value of Δx and Δy.   C Δx = A + C Δy = B R   B A

Vectors: magnitude Can be determined using the following equation:   C R   B R = √Δx2 + Δy2 A Pythagorean Theorem