# Vectors

## 2. Vectors

### 2.1 Vector and Scalar Quantities

A scalar quantity has magnitude but not direction

Examples:

• Distance
• Speed (average speed = total distance / total time)
• Mass (amount of matter)
• Temperature
• Density (mass / volume)
• Energy
• Pressure (force / area)

A vector quantity has magnitude and direction

Examples:

• Displacement
• Velocity (average velocity = total displacement / total time)
• Acceleration (average acceleration = change in velocity / time taken)
• Force (measured in newtons, N)
• Weight (the force of gravity. On this planet, 1 kg weighs 9.8 N)
• Momentum (Mass · Velocity)

In textbooks, vector quantities are sometimes shown in bold type. When writing by hand, you can put an arrow over the quantity to emphasize that it is a vector quantity.

### 2.2 Rectangular components of a vector

Any single vector can be replaced by two components that add by vector rules to form the original vector. This is called 'resolving the vector' and is most useful when the component vectors are perpendicular to one another e.g. horizontal and vertical. Such vectors can be called the 'rectangular components'.

### 2.3 Find the magnitude and direction of a vector

I think this was included in the ITESM syllabus by mistake, for the magnitude and direction of a vector are almost always given in physics problems!

### 2.4 Calculate the resultant vector both graphically and analytically

Take care when adding vectors since the direction must be taken into account – if the vectors are not parallel then you will need to draw a scale diagram or use ‘components’ (subject of a later lesson). The resultant (vector sum) of two vectors can be determined from a vector diagram drawn to scale.