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This lecture covers the concept of the Euclidean norm in R², including its properties and interpretation. It also delves into the triangular inequality, explaining its significance and applications in determining relationships between vectors. The instructor demonstrates how to calculate distances between points in R² and emphasizes the triangular inequality's role in geometric interpretations. Additionally, the lecture explores the properties of the Euclidean distance, providing insights into the relationships between vectors and the implications of the triangular inequality in various scenarios.