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This video explains the paralelogram method and the cosenos method for adding vectors. In the paralelogram method, a perpendicular line is drawn to the vector representing the river's speed, and a line parallel to the vector representing the boat's speed is drawn. This results in a paralelogram. The magnitude of the resultant vector is 120 mph. In the cosenos method, the resultant vector is equal to the vector representing the river's speed times the vector representing the boat's speed divided by the square of the magnitude of the vector representing the river.

**00:00:00**In this video, the paralelogram method for adding vectors is explained. First, a situation is introduced, in which two blue lines represent a river. A boat is crossing the river at a speed of 40 mph. Then, the river's speed is represented by the blue vector, and the boat's speed is represented by the green vector. The boat's speed is 30 mph in a direction perpendicular to the vector representing the river's speed. The magnitude of this vector is 40 mph. Additionally, the boat's speed is also 30 mph in a direction at a 60 degree angle relative to the vector representing the river's speed. To determine the magnitude of the resultant vector, the paralelogram method is used. A perpendicular line is drawn to the vector representing the river's speed, and a line parallel to the vector representing the boat's speed is drawn. This results in a paralelogram. The magnitude of the resultant vector is 120 mph. Next, the cosenos method is used to determine the magnitude of the resultant vector. The resultant vector is equal to the vector representing the river's speed times the vector representing the boat's speed divided by the square of the magnitude of the vector representing the river**00:05:00**The video explains the sum of vectors using the method of rectangular components. It then goes on to explain the magnitude of a vector's result using the teorema of los cosenos.

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