Vetores - Aula 05 (Lei dos Cossenos)

Summary

In this lesson, Professor Davi explains how to add two vectors using the parallelogram rule and the law of cosines. He begins by demonstrating how to graphically add vectors by drawing parallel lines and creating a parallelogram. The professor also delves into how to apply the law of cosines to calculate the resultant vector, emphasizing the importance of understanding the angle between vectors. He explains various cases, such as vectors in the same direction or perpendicular, and how to solve them. The video concludes with an example involving vectors with a 60-degree angle, showing the process to find the vector sum.

Takeaways

• 😀 The parallelogram rule is a method used to add two vectors, and the resulting vector is determined by constructing a parallelogram using the two vectors.
• 😀 To apply the parallelogram rule, first draw dotted lines parallel to each of the vectors and complete the parallelogram shape.
• 😀 The vector sum is the diagonal of the parallelogram, which is drawn from the origin to the point where the dotted lines intersect.
• 😀 The resulting vector, also known as the vector sum or the resultant vector (R), can be calculated using the law of cosines in certain cases.
• 😀 When applying the law of cosines, the formula is: R² = A² + B² + 2AB cos(θ), where A and B are the magnitudes of the vectors, and θ is the angle between them.
• 😀 A common question arises about the use of the plus sign in the law of cosines when adding vectors, as students are accustomed to seeing a minus sign in some situations.
• 😀 The reason for the positive sign in the law of cosines is because it applies to the angle between the two vectors, and this angle is supplementary to the angle used in the traditional cosine rule.
• 😀 When adding vectors that are not perpendicular (90°), the law of cosines must be used to find the magnitude of the resultant vector.
• 😀 In special cases, such as vectors being parallel or forming a 90° angle, alternative methods like Pythagoras' theorem or simple addition can be used instead of the law of cosines.
• 😀 Understanding vector addition involves recognizing when to use different methods, such as the parallelogram rule, Pythagoras' theorem, or the law of cosines, based on the angle between the vectors.
• 😀 The class ends with an example where two vectors with a 60° angle are added, and the final resultant vector is calculated using the law of cosines and approximations for practical use in multiple-choice questions.

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