The reason for the variation in Alpine vegetation between the western and eastern Himalayas is primarily due to Option 3: eastern Himalayas receive more monsoon rainfall than the western Himalayas. However, it`s important to note that there may be some additional factors contributing to this variation as well.

1. Monsoon Rainfall: The monsoon plays a crucial role in determining the distribution of vegetation in the Himalayas. The eastern Himalayas receive a higher amount of rainfall during the monsoon season compared to the western Himalayas. This increased rainfall in the east provides more moisture for vegetation growth, allowing alpine plants to thrive at higher elevations.

2. Rain Shadow Effect: The distribution of precipitation in the Himalayas is influenced by the rain shadow effect. When moist air from the Indian Ocean encounters the Himalayan mountain range, it is forced to rise, resulting in orographic precipitation on the windward side (southern slopes) of the mountains. As the air moves over the mountain range and descends on the leeward side (northern slopes), it loses moisture, creating a rain shadow. The western Himalayas lie in the rain shadow of the main Himalayan range, which leads to drier conditions and lower rainfall compared to the eastern Himalayas.

3. Altitude and Temperature: Temperature decreases with increasing altitude, and this has a significant impact on vegetation distribution. The western Himalayas have lower altitudes on average compared to the eastern Himalayas. As a result, the lower elevations in the west have higher temperatures, which can limit the growth of alpine vegetation. In contrast, the higher altitudes of the eastern Himalayas provide cooler temperatures that are more suitable for alpine plants.

4. Latitude and Proximity to the Sea: Option 2 suggests that the eastern Himalayas are nearer to the Equator and sea coast than the western Himalayas. While this statement is true to some extent, the primary factor affecting vegetation distribution in the Himalayas is the monsoon rainfall, as discussed earlier. However, the proximity to the sea and lower latitudes can influence the moisture content and temperature of the air masses, which in turn affect precipitation patterns and the growth of vegetation.

Option 1 (height difference) and Option 4 (fertility of rocks) are not significant factors contributing to the variation in Alpine vegetation. While there may be some slight elevation differences between the western and eastern Himalayas, it is the rainfall and temperature patterns that play a more prominent role. Similarly, the fertility of rocks does influence vegetation to some extent, but it is not the primary reason for the variation in Alpine vegetation between the two regions.

In conclusion, the primary reason for the variation in Alpine vegetation between the western and eastern Himalayas is the difference in monsoon rainfall. The eastern Himalayas receive higher rainfall due to their location and the influence of the monsoon, providing more moisture and favorable conditions for alpine plants to grow at higher elevations.