Scalars and vectors are two types of quantities used in math and physics that differ in how they are described.
Magnitude
Firstly, let's define magnitude. Magnitude is a unit of measurement that describes the size or intensity of an event or the size of an object relative to others. It is the size or quantity of a physical property indicating how much of something is present without considering its direction. It is expressed in a numerical value of a quantity, such as a force's strength or an object's speed.
Scalar Magnitudes
Mass
Temperature
Time
Distance
Vector Magnitudes
Displacement
Velocity
Force
Acceleration
Direction
Direction is the location of something relative to something else, the orientation or path of the motion of an object. Direction can be in both relative terms, or they could be cardinal directions:
Relative terms: Upwards, downwards, leftwards, rightwards, forwards, backwards, or sideways
Cardinal directions: north, south, east, or west
In addition, sometimes direction can be referred to as positive or negative, whereby positive is generally considered rightwards on the x-axis or upwards on the y-axis in motion and acceleration.
The negative is leftwards on the x-axis and downwards on the y-axis, as seen in the illustration to the right.
Scalar
Scalars are quantities that only have magnitude (or size), and the examples of scalars are:
Volume
Density
Speed
Energy
Mass
Time
Distance
Temperature
Length
Power
Area
To compare two scalar quantities, you only have to compare the magnitude, as a scalar is a quantity with only magnitude. Scalar quantities are one-dimensional quantities, and vectors are two-dimensional quantities, which is why it's not possible to add the two together.
An example of a scalar temperature is that in London, it is currently 10 degrees Celsius; for a mass, the dumbbell is 5 kilograms (kg), and for energy, the lightbulb uses 100 joules of energy every second.
Distance could be that David walked a distance of 1000 meters, and for density, one could say the seawater is 1088 kg/m3. As one can see, none of the above states any direction, just magnitude.
Vector
Vectors have both magnitude (or size) and direction. When comparing two vector quantities of the same type, you must compare both the magnitude and the direction. Examples of vector quantities are:
Displacement
Acceleration
Force
Momentum
Weight
Velocity of light
Thrust
Drag
Lift
Torque
Impulse
Magnetic field
Electric field
For example, for displacement, one could say 50 kilometres (km) east, an object has a velocity of 11 meters per second (m/s) upwards, the car has an acceleration of 9.8 meters per second squared (m/s2) downwards, the object has a momentum of 250-kilogram meters per second (m/s) southwest, or an object has a force of 30 newtons (N) in the negative direction (downward).
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