Vectors can be visually represented as arrows, where the length of the arrow indicates the magnitude and the direction in which the arrow points indicates the vector’s direction.

A vector is defined as a quantity that possesses both magnitude (or size) and direction. When we graphically represent vectors, we use arrows: the length of the arrow corresponds to the vector’s magnitude, while the direction of the arrow denotes the vector’s direction.

To draw a vector, begin at a specified point known as the tail of the vector, and draw an arrow extending to another point, which is referred to as the head of the vector. The length of the arrow should be proportional to the vector’s magnitude. For instance, if you are illustrating a velocity vector of $5 \, \text{m/s}$, you might choose a scale where $1 \, \text{cm}$ on your paper represents $1 \, \text{m/s}$. Consequently, you would draw an arrow that is $5 \, \text{cm}$ long.

The direction of the arrow is crucial, as it represents the vector’s orientation. For example, if a car is traveling east at $5 \, \text{m/s}$, you would draw an arrow pointing to the right, assuming you are using a standard map orientation where up corresponds to north and right corresponds to east.

When adding vectors graphically, you position the tail of the second vector at the head of the first vector. From the tail of the first vector, you then draw a new vector that extends to the head of the second vector. This newly drawn vector represents the sum of the two vectors.

In the case of vector subtraction, you can conceptualize it as adding the opposite of the vector you wish to subtract. For example, to subtract vector $B$ from vector $A$, you would add $-B$ to $A$. Graphically, this involves reversing the direction of vector $B$ and then following the same procedure as for addition: placing the tail of the modified $B$ at the head of $A$ and drawing a resulting vector from the tail of $A$ to the head of the modified $B$.

It is essential to maintain a consistent scale when representing vectors graphically. If you decide that $1 \, \text{cm}$ corresponds to $1 \, \text{m/s}$, you must apply that same scale to all vectors you draw. Additionally, it is important to clearly indicate the direction of each vector, which can be accomplished by using a compass rose or by explicitly stating the direction in words.