#### Additing Vectors Graphically

Take your time when using this technique.

It requires accuracy when scaling, measuring and drawing vectors. Only if you're accurate you will obtain correct results.

**Step-by-step approach:**

- Choose a scale according to the given information
- Start with a set of reference axis and draw the first vector using a ruler to draw its magnitude to sale and a protractor to report its direction.
- At the head of the vector draw a small cross. This is a new reference axis to guide you in drawing successive vectors.
- Draw the second vector (and the third if necessary) using steps 1 to 3.
- Draw the resultant vector from the tail of the first vector to the head of the last vector.
- Use a ruler and protractor to report the magnitude and direction of the resultant vector properly.

**Example:**

A pigeon flies 5 km [N30^{0}E], then 2.5 km [E40^{0}S]. Calculate its final displacement.

**Solution:**

Step 1 - choose an appropriate a scale such as:*scale = 1cm = 1 km; *therefore: **a** = 5 cm [N30^{0}E], and **b **= 2.5 cm [E40^{0}S].

Step 2 - draw vectors **a **and **b** to scale

Step 3 - join the tail of vector **a** to the head of vector ** b** to find the resultant vector **c**.

Step 4 - measure resultant vector **c** using a ruler and convert to real-time units using your scale.

Step 5 - use a protractor to measure and report the direction of resultant vector** c**.

Step 6 - Conclusion - The final displacement of the pigeon is **c** = 5.2 km [E30^{0}N]

Refer to the diagrams below:

Figure 1 - Steps 1 to 4

Figure 2 - Steps 5 & 6