Vectors and scalars

By the end of this chapter you should be able to:

•describe the difference between vector and scalar quantities and give examples of each;•add and substract vectors by a graphical technique, such as the parallelogram rule;•find the components of a vector along a given set of axes;•reconstruct the magnitude and direction of a vector from its given components;•solve problems with vectors.

Vectors and scalarsSome quantities in physics, such as time, distance, mass, speed, temperature, etc., just need one number to specify them. These are called scalar quantities.

On the other hand, many quantities are fully specified only if, in addition to a number, a direction is given. Examples are velocity, acceleration, force, etc. These are called vector quantities.

Vectors Scalars

Displacement Distance

Velocity Speed

Acceleration Mass

Force Time

Momentum Density

Electric Field Electric Potential

Magnetic Field Energy/Work

Gravitational Field Temperature

Torque Electric charge

Vectors

A vector is represented by a straight line with an arrow at one end. The direction of the arrow represents the direction of the vector and the length of the line represents the magnitude of the vector. To say that two vectors are the same means that both magnitude and direction are the same.

Two vectors that have the same magnitude but are opposite to each other in direction are the negatives of one another.