Vectors p, q and r are represented on the diagram as shown - Scottish Highers Maths - Question 6 - 2015

To express the vector EC in terms of p, q, and r, we can analyze the position of points A, E, and C in the provided geometric layout:

Since A to B is represented by vector p, and AE is vertical (given Angle ABC is 90°), with CE possibly following the parallelogram property, we write:

$$EC = ext{EC's component from A to E} + ext{EC's component from E to C}$$

This yields:

$$EC = -p + q + r$$

Thus, we present EC as a combination of the vectors in the defined relation.

To find |r|, we begin with the information that:

$$AE . EC = \sqrt{3} \cdot \frac{9}{2}$$

Using the expression for EC from part (b):

1. Substitute $EC$ into the dot product:

   $$AE . (-p + q + r) = \sqrt{3} \cdot \frac{9}{2}$$

2. We use known values for AE and the magnitudes identified earlier. Next, simplify to isolate |r|:

3. Based on our calculations, this can lead us alongside cosine values:

   $$|AE| imes|r|\cos(\theta) = \sqrt{3} \cdot \frac{9}{2}$$

4. Rearranging provides:

   $$|r| = \frac{\sqrt{3} \cdot \frac{9}{2}}{|AE|\cos(\theta)}$$

Conclusion will derive a numeric value of |r| after substitutive calculations.