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The video, titled "Class 12 Vector Live | Eclat Coaching: Vector Cross Products (Area of Parallelogram & Triangle)", features a teacher conducting a live online math class, primarily focusing on vector cross products and their applications (1:07:00). The instructor uses an interactive and engaging style, encouraging student participation by offering a ₹100 prize for the first correct answer (12:16-12:51) and motivating students to actively solve problems. Key topics covered in the session include: Vector Cross Product (A x B): The fundamental concept of calculating the cross product of two vectors is demonstrated and practiced (47:21). Modulus of a Vector: How to find the magnitude (modulus) of the resulting vector from a cross product (30:07). Area of a Parallelogram: The application of the cross product to find the area of a parallelogram, using the modulus of the cross product of its adjacent sides (43:05). Area of a Triangle: A detailed explanation that the area of a triangle is half the area of a parallelogram formed by two of its sides, demonstrated by `1/2 |A x B|` (43:34-44:19). This topic is emphasized as a 100% confirmed question for two marks in board exams (44:32-44:47). The class is highly interactive, with the teacher frequently calling out student names for their answers and encouraging them (18:11, 21:57, 34:08). Homework questions (7, 8, 9, 10) for practicing the "Area of Triangle" concept are assigned at (40:16) and again at (1:11:00). The teacher also stresses the importance of practice to avoid common errors (1:11:42). The next topic, Unit Vector Perpendicular to the Vector, is briefly introduced at the end (1:15:17).