To solve this problem, we will use the concept of the slope and tangent of the angle subtended by the line segments at the origin.

Given points: $$(5,2)$$ and $$(2,a)$$

The slope of the line joining the origin and $$(5,2)$$ is:

$$m_1 = \frac{2-0}{5-0} = \frac{2}{5}$$

The slope of the line joining the origin and $$(2,a)$$ is:

$$m_2 = \frac{a-0}{2-0} = \frac{a}{2}$$

The line segment joining these points subtends an angle $$\theta = \frac{\pi}{4}$$ at the origin.

According to the tangent formula for the angle between two lines:

$$ \tan \theta = \left| \frac{m_2 - m_1}{1 + m_1 m_2} \right| $$

Here, $$\theta = \frac{\pi}{4}$$ so, $$\tan \left( \frac{\pi}{4} \right) = 1$$. Therefore,

$$ 1 = \left| \frac{\frac{a}{2} - \frac{2}{5}}{1 + \left(\frac{2}{5} \cdot \frac{a}{2}\right)} \right| $$

This simplifies to:

$$ 1 = \left| \frac{\frac{5a - 4}{10}}{1 + \frac{2a}{10}} \right| $$

Multiplying both the numerator and denominator by 10 to simplify:

$$ 1 = \left| \frac{5a - 4}{10 + 2a} \right| $$

This leads to two equations due to the absolute value:

1. $$ 5a - 4 = 10 + 2a $$

$$ 3a = 14 $$ $$ a = \frac{14}{3} $$

2. $$ 5a - 4 = -(10 + 2a) $$

$$ 5a - 4 = -10 - 2a $$ $$ 7a = -6 $$ $$ a = -\frac{6}{7} $$

Thus, the possible values of $$a$$ are $$\frac{14}{3}$$ and $$-\frac{6}{7}$$.

The product of these values is:

$$ \left| \frac{14}{3} \times -\frac{6}{7} \right| $$ $$ = \left| -\frac{84}{21} \right| $$ $$ = \left| -4 \right| $$ $$ = 4 $$

Therefore, the absolute value of the product of all possible values of $$a$$ is 4.

Answer: Option A