Parallelogram Law of Vector Addition | Infinity Learn

Summary

This video explains the concept of vector addition using two methods: the parallelogram law and the triangle law. It begins with an example of a boat crossing a river, illustrating how the boat's actual velocity results from the combination of its engine speed and the river's current. The script demonstrates the application of the parallelogram law to find the resultant velocity of two perpendicular vectors, followed by the triangle law as an alternative method. Both laws give the same result, and the video concludes by previewing how vector subtraction will be covered in the next lesson.

Takeaways

• 😀 The boat crossing a river will reach the opposite bank at a point to the right of the intended destination due to the velocity of the river.
• 😀 The boat's velocity is influenced by two factors: the velocity of the boat's engine (v1) and the velocity of the river (v2).
• 😀 The boat's actual velocity (v3) is the vector sum of v1 and v2.
• 😀 To calculate the resultant velocity vector (v3), the parallelogram law of vector addition is used.
• 😀 In the parallelogram law, the sum of two vectors is represented by the diagonal of a parallelogram formed by the vectors.
• 😀 The parallelogram law can be applied to find the magnitude and direction of the resultant velocity vector of the boat.
• 😀 The triangle law of vector addition also gives the same resultant vector as the parallelogram law.
• 😀 To apply the triangle law, one vector is moved such that its initial point coincides with the terminal point of the other vector.
• 😀 Both the parallelogram and triangle laws are equivalent for vector addition, and they produce the same result.
• 😀 The lesson emphasizes how to add vectors using both the parallelogram and triangle laws and introduces the concept of vector subtraction in the next lesson.

Q & A

What happens to the boat when it crosses the river perpendicular to the flow?

The boat will reach the bank somewhere to the right of the intended point due to the influence of the river's velocity along with the boat's engine velocity.

How is the actual velocity of the boat determined?

The boat's actual velocity is the resultant of the velocity of the boat's engine (v1) and the velocity of the river (v2). This is found by vector addition.

What is vector v3 in the context of the boat's motion?

Vector v3 represents the boat's actual velocity, which is the vector sum of the boat's engine velocity (v1) and the river's velocity (v2).

What is the Parallelogram Law of Vector Addition?

The Parallelogram Law states that the sum of two vectors is represented by the diagonal of the parallelogram formed by the two vectors in magnitude and direction.

How do you find the resultant vector using the Parallelogram Law?

To apply the Parallelogram Law, you draw two vectors parallel to the given vectors and form a rectangle. The diagonal of the rectangle represents the resultant vector.

What happens when vectors are not drawn from the same initial point?

If two vectors, such as c and d, do not have the same initial point, the vector sum is found by moving one vector parallelly until both vectors have the same initial point. Then the Parallelogram Law is applied.

What is the Triangle Law of Vector Addition?

The Triangle Law states that if you move one vector such that its initial point coincides with the terminal point of the other vector, the third side of the resulting triangle represents the vector sum.

What is the difference between the Parallelogram and Triangle Laws?

Both the Parallelogram and Triangle Laws provide the same resultant vector; however, they approach vector addition differently. The Parallelogram Law uses a parallelogram, while the Triangle Law uses a triangle formed by the vectors.

Are the Parallelogram and Triangle Laws of Vector Addition equivalent?

Yes, both the Parallelogram and Triangle Laws of Vector Addition are equivalent and give the same resultant vector.

What will be covered in the next lesson after vector addition?

The next lesson will cover how to subtract two vectors, building on the concept of vector addition.