Why Vectors? A vector allows us to describe both a quantity and a direction of an object. A vector is a quantity that has both magnitude and direction. A scalar is a number indicated by the size or magnitude of the quantity. Think of times when a vector might be used: the speed and direction of an airplane, the navigation of the path of a ship, or the path of a ball after being thrown or kicked.

Vector or Scalar? A car traveling 40 km/h. 2. A motorcycle traveling 60 km/h due north. 3. A train traveling 40 km/h east to the beach. 4. A child’s weight on a scale.

Which of the following would NOT be a vector? 1. A boat traveling 50 km/h north An object falling straight down at 15 km/h A worker pushing an object with a force of 30 newtons #3 There is a magnitude, but no direction!

Distance – tells us how far something has moved (example the odometer in a car tells us how much distance the car has travelled since it was made). (m, km, etc) Speed – tells us how much distance has been travelled per second, minute, or hour. (km/h, m/s) Scalar quantities

When you draw vectors B Terminal Point or tip Initial Point or tail A A vector is a quantity that has both magnitude (size of the quantity) and direction.

Displacement – the vector equivalent of distance Displacement – the vector equivalent of distance. It tells us how far something has moved in a specific direction. If the object moves in the opposite direction velocity can even be negative. Velocity – is a vector quantity. It tells us how much displacement there has been per second or hour. Vector quantities

Adding Vectors When two or more vectors are added, their sum is a single vector called the resultant. One method for adding vectors is called the triangle method and is illustrated graphically below. One method of adding vectors is called “tip to tail”. Think of the tip as an arrow tip and the tail is the initial point. To determine the resultant of a and b, draw the vectors so that the tip of a touches the tail of b. These vectors are opposites! How would you determine a – b? The resultant is the vector from the tail of a to the tip of b.