Vectors

A vector is a quantity that has a magnitude and a direction. Examples of quantities that have a magnitude and direction are displacement, velocity, acceleration and force. With displacement, you can specify the direction as well as the net distance moved by the object.

The difference between speed and velocity is that speed only specifies the speed with which any object is moving but doesn't establish the direction the object is moving in. However, velocity specifies the magnitude, which includes the speed and the direction. Similar to velocity, we have acceleration. A form of acceleration is gravity, and we know that this always acts downwards and is always approximately. 9.81 m/s2 . Well atleast on Earth. It is 1/6th  of this on the moon.

An example of force is weight. Weight also acts downwards and is calculated as mass multiplied acceleration.

Vectors are graphically represented by a pointed line segment with the length of the line denoting the magnitude of the vector and the pointed arrow showing the direction of the vector. We can move around a vector as doing this doesn't change the magnitude or the direction of it.

Two vectors are said to be equal if they both have the same magnitude and direction even if they are in different locations. Vectors are denoted by arrow marks above the letter

The as follows vectors  and  are starting in different locations. Since the direction and magnitude of the arrows are the same, they are equal:

In a 3D coordinate system, a vector is specified by the coordinates with respect to the coordinate system. In the example as follows, the vector  is equal to (2, 3, 1) and is also denoted as is denoted as:

 =