A vector is orthogonal if A · B = 0. For B = 3i - 2j, A · B = 6 - 6 = 0.

The Industrial Revolution led to a significant rise in urbanization as people moved to cities for factory jobs, transforming social and economic structures.

During the Mauryan Empire, particularly under Ashoka, there was a significant promotion of Buddhist education and the establishment of monasteries as centers of learning.

The Gupta period is known for promoting trade and commerce, leading to economic prosperity and cultural development.

The Mughal Empire promoted trade and commerce, leading to a flourishing economy and cultural exchange.

Ancient Athens is known for its system of direct democracy, where citizens participated directly in decision-making.

A key feature of the Harappan Civilization was its complex urban planning, including well-laid streets and advanced drainage systems.

Mass production was a key feature of the Industrial Revolution, allowing for the efficient manufacturing of goods.

The British colonial planning strategies primarily focused on infrastructure development aimed at resource extraction to benefit the British economy.

The establishment of the General Board of Health in 1848 marked a significant step in public health reforms in Britain, focusing on sanitation and disease prevention.

The emergence of factory-based production was a key outcome of the Industrial Revolution in the 18th century, transforming economies and societies.

The Sepoy Mutiny of 1857 was caused by a combination of economic exploitation, religious insensitivity, and political annexation, making all options relevant.

British colonial policies led to the deindustrialization of India, as traditional industries were undermined by British imports and policies favoring British manufacturers.

The French Revolution led to the spread of revolutionary ideas across Europe and the end of feudalism in France.

The Green Revolution in India during the 1960s led to increased food production through the use of high-yield variety seeds and chemical fertilizers.

The Industrial Revolution led to the rise of the middle class as new jobs and economic opportunities emerged in urban areas.

The Industrial Revolution led to the rise of factory-based economies, transforming production and labor.

The Treaty of Nanking, signed in 1842, was a major consequence of the First Opium War, marking the beginning of the 'Century of Humiliation' for China.

The Treaty of Tientsin (1856) opened several Chinese ports to foreign trade, significantly impacting China's border management and foreign relations.

The Zimmermann Telegram, in which Germany proposed a military alliance with Mexico against the U.S., was a significant factor in the U.S. decision to enter World War I.

While the Green Revolution increased agricultural productivity, it also led to widening social inequalities, as wealth became concentrated among a few landowners.

The Cripps Mission was largely rejected by Indian leaders, as it did not meet their demands for complete independence.

The Industrial Revolution led to the rise of factory-based economies, transforming production methods and urbanizing populations.

The major outcome of the Round Table Conferences was the Government of India Act 1935, which provided for a greater degree of self-governance.

The Round Table Conferences led to the Government of India Act 1935, which provided for a federal structure in India.

The formulation of the laws of planetary motion by Johannes Kepler was a significant scientific achievement during the Renaissance.

Taxila was a prominent trade center during the Maurya period, known for its educational institutions and trade routes.

The Round Table Conferences led to the Government of India Act 1935.

The seed drill, invented by Jethro Tull, was a significant agricultural innovation during the Industrial Revolution that allowed for more efficient planting of seeds.

World War II led to the emergence of the United States and the Soviet Union as superpowers, resulting in the Cold War, a period of geopolitical tension.