Vector Addition: Calculate Magnitude of Sum

• joej24
In summary, when a vector of magnitude 20 is added to a vector of magnitude 25, the magnitude of the resulting vector can range from 5 to 45. The correct answer is 12.
joej24

Homework Statement

A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:
a. zero
b. 3
c. 12
d. 47
e. 50

c ^2 = a^2 + b^2

The Attempt at a Solution

I was not entirely sure on what to do. I tried using the Pythagorean theorem to find the resultant of the 2 vectors and got 32. ( c ^2 = 20^2 + 25^2).
The answer by the way is C.

Thanks!
Joe

Try do add the vectors in different ways. Then you will get a possible maximal and a minimal value for the magnitude of the resulting vector. All but one possible answers are outside of this region.

okay. I got it. The max magnitude of their addition would be when they are parallel in the same direction. mag would = 45. The min would be when they are parallel in the opposite direction. mag would = 5. Therefore the answer is 12. Thanks!

Good.

I would like to clarify and explain the concept of vector addition and how to calculate the magnitude of the sum. Vector addition is the process of combining two or more vectors to obtain a single vector, known as the resultant. The magnitude of the resultant is calculated using the Pythagorean theorem, as you correctly attempted. However, it is important to note that the magnitude of the resultant is not simply the sum of the magnitudes of the individual vectors.

In this case, the magnitude of the sum would be the square root of (20^2 + 25^2) = 32.0156. This means that the answer is not exactly 12, but rather a value close to it. Therefore, the correct answer is option C.

It is also important to mention that the direction of the resultant vector is determined by the direction of the individual vectors being added. This can be calculated using trigonometric functions such as sine and cosine.

In conclusion, when adding vectors, it is crucial to understand the concept of vector addition and how to calculate the magnitude and direction of the resultant. I hope this explanation helps in understanding the solution to this problem.

What is vector addition and why is it important?

Vector addition is the process of combining two or more vectors to determine the magnitude and direction of their sum. It is important because it allows us to accurately calculate the resulting motion or force when multiple vectors are acting on an object.

What is the formula for calculating the magnitude of vector addition?

The formula for calculating the magnitude of vector addition is the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the individual vector components.

How do you represent vectors in a coordinate system?

Vectors can be represented in a coordinate system by using arrows. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vector addition involves combining both the magnitude and direction of vectors, while scalar addition only involves adding the numerical values of scalars. Vectors also follow the laws of vector addition, such as the commutative and associative properties, while scalars do not.

What are some real-world applications of vector addition?

Vector addition is used in various fields, such as physics, engineering, and navigation. It can be used to calculate the net force on an object, determine the resultant velocity of a moving object, and plot the path of a moving object. It is also used in navigation systems to determine the direction and speed of an object's movement.

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