Representing a vector
- 1. REPRESENTING A VECTOR …A Quick Review
- 2. WHAT IS A VECTOR? • While a scalar quantity has only magnitude (size), a vector is a quantity which has both magnitude and direction. mathisfun.com • Examples of vector quantities (scalar equivalent in brackets) : weight (mass), displacement (distance), velocity (speed). **the velocity of a vehicle is its speed in a particular direction.
- 3. REPRESENTING A VECTOR • Vectors can be represented geometrically by arrows. The length of the arrow represents the size of the vector and the direction of the arrow gives the direction of the vector. • An example of this is “Lisa walks 8km due east” 8 km The arrow is pointing east – the same direction as Lisa’s path and the length of the arrow is representative of how far she walked
- 4. REPRESENTING A VECTOR CONT’D • Vectors can also be represented in a column matrix 𝑥 𝑦 • Where x is the horizontal shift of the vector and y is its vertical rise The vector shown with start point P and end point Q can be represented as (i) 𝑃𝑄 (ii) bold letters PQ or (iii) a single common letter 𝑝 𝑜𝑟 𝒑.
- 5. REPRESENTING A VECTOR CONT’D • Remember the direction of the vector is important! • When representing a vector we use positive (+) and negative ( – ) signs to indicate direction. • On the horizontal axis : • A movement from the start point to the right is a positive movement • A movement from the start point to the left is a negative movement • On the vertical axis: • Moving up is a positive movement • Moving down is a negative movement Remember to count the squares to get the magnitude!
- 6. REPRESENTING A VECTOR CONT’D Lets try one together! Can we represent the vector shown below? In the vector shown the start point is S and the end point is T (we can see that from the direction of the arrow) We have counted the number of squares on both the horizontal and vertical component of the vector the vector is moving to the right (+) and up (+) We can therefore represent this vector as
- 7. The End!