A scalar has only a magnitude (size) whereas a vector has both a magnitude and a direction.
Example;
- 9 ms-1 is a scalar it has magnitude only (speed is a scalar)
- 9 ms-1 North is a vector as it has both a magnitude and a direction (velocity is a vector)
Examples of Scalars
distance, area, volume, speed, time, mass, energy, power, temperature, electric potential
Examples of Vectors
displacement, velocity, acceleration, force, momentum, electric field strength, magnetic field strength
Adding vectors to find the resultant vector
Vectors which act in the same direction or whose directions are exactly opposite to each other are easy to add together but you must take account of their directions.
Example 1. Two 5N forces acting to the right add together to give a 10N force acting to the right.
Example 2. A 10N force acting to the right and a 5N force acting to the left add together to give a 5N force to the right.
Adding vectors which act at 90o to each other
We can use Pythagoras’ theorem and trigonometry to find the resultant of the vectors and the direction it is acting in.
Two forces of 41N and 60N act at 90o to each other.
STEP 1 – calculate the resultant force R
STEP 2 – calculate the angle ?
