Reasons for alternative sea route to India - Vasco de Gama's voyage

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Vasco de Gama, seriousfacts.com
Well developed cottage industries in India, besides vast natural resources  in the1400s attracted the Europeans and they badly needed them, including  raw materials for their factories. Indian goods were in great demand in Europe – cotton, earthen utensils, spices  such as  cardamom, cloves, pepper, cinnamon, etc got the special attention.  In 1453, with the fall of Constantinople in Asia Minor, which was the bastion of Christianity, the autocratic Islamic Ottoman Empire not only closed the land route to India and other eastern countries, but also were hostile to the Christian communities there. The sea route eliminated the risk of crossing the disputed Mediterranean sea and the notorious Arabian peninsula. This blockade marked the end of Roman rule of Byzantine Empire. It was a great blow to the Christians, European traders and others.  Prior to the first discovery of the sea route to India by Vasco de Gama, Europe, especially Venice and Geneva had been enjoying lucrative trade with the Indian sub continent. As an alternative sea route to India and other eastern countries had to be found, there was a big competition among the Europeans to expand their business to other overseas countries as well. Part of the mission was to spread the Gospel of Christianity'.  
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The massive blow to  Christendom spurred the age of discovery as Europeans were seeking alternative routes to eastern countries by sea along with the goal of forging alliances with per-existing Christian nation.  Sea  journey during the medieval period was extremely hazardous. Life on the high seas was tough and deaths were common and frequent. Vasco da Gama had begun his voyage with 130 people  but  returned to Portugal with only 59 -  more than half the people perished midway, besides losing two of his support ships along the African coast. Sailors  had to stay close to the shore and generally would not sail too far into the unpredictable mid sea. As for sailing, under normal weather condition, speed of the ship would not go beyond 10 to 12 kilo meter/hr.  When it comes to food  and water, they had to sustain on a strict diet of biscuits and fish and extremely rationed supply of potable water. If they ran out of fresh water they would face dehydration and near death. There was always the danger of running out of drinking water. At sea they had to tackle exertion and fatigue  constant exposure to the scorching Sun - an Herculean task. To cap it all,  they had to tackle unpredictable sea conditions with impending giant waves 
Tomb of Vasco da Gama in the Jerónimos Monastery in Belém, Lisbon military.wikia.com
Vasco de Gamais sea route to India. en.wikipedia.org
In the face of these bottle-necks, competition and naval adventures, in a way, inspired the highly motivated  Europeans to use better technology in ship-building. They learned to build sturdy ocean-going ships to withstand long, rough journey in the sea, better food, water storage facilities, better sails, navigational instruments, spacious galley, etc. They also had a better defence mechanism built aboard the ship to tackle the menace of sea pirates and threats from other sea-faring countries. Christopher Columbus, the Italian Navigator whose mission was to find a sea route to India, instead landed in the West Indies; thus a vast new world - 'the  Americas' was accidentally discovered in 1492. After decades of navigators  trying hard to reach India with thousands of lives and dozens of vessels lost in shipwrecks and attacks, Gama landed at Calicut (Kozhikode now in the state of  Kerala- Kappad beach on the Malabar coast of India on May 20,1498. Vasco da Gama (1469-1524), with sheer grit and determination  performed this rare, unprecedented feat of navigating from Lisbon in Portugal to Calicut in India, the entire journey lasting over ten months. In the process, unwittingly he connected Europe with Asia through  a new sea route. Discovery of American continent by Columbus  and this one by Gama are momentous events in sea-faring and world history, and  thus they laid the foundation for the establishment of money-spinning colonies by Britain, France and other European countries. " Vast Indian revenues subsequently financed the British imperialism and the British Empire.

Thus, the necessity and motivation, besides better ship building techniques to find an alternative sea route to India, consequently led to the discovery of a new world – South and North American continents and new mercantile trades. 
As for new sea route to India, Europeans thought it would serve several purposes after the fall of Constantinople. To restore the highly profitable trade with India and other eastern countries and to spread Christianity in a new land to make up the loss of Constantinople - once a huge Christian stronghold. They had no idea about India's vast riches, advanced culture and languages, and excellent knowledge in maths, astronomy, construction of buildings and temples, etc.

Ref:

Subrahmanyam, Sanjay (1997). The Career and Legend of Vasco da Gama. Cambridge University Press. ISBN 978-0-52