Finding the magnitude of the resultant vectors

In summary, the magnitude of the resultant vector S + T + U is 4.9. To get this answer, the x and y values of the three given vectors were added together, and then the pythagorean theorem was used to find the magnitude of the resultant vector.
  • #1
fxsnowy
3
0
I need help on how to solve this

Homework Statement



Three vectors, expressed in Cartesian coordinates are :
S -> x( -3.5), y(+4.5)
T -> x(0), y(-6.5)
U -> x(+5.5), y(-2.5)

what is the magnitude of the resultant vector S + T + U?

The answer, according to my answer sheet is 4.9, but I don't know how to get that answer.

Any help is greatly appreciated
 
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  • #2
What is the magnitude of a vector?
 
  • #3
Firstly, how would you go about adding one vector to another?
 
  • #4
Solution.

There might be different ways to do it but here's how I did it.

First, add up all of the x values: (-3.5) + 0 + 5.5 = 2
then, add up all of the y values: 4.5 - 6.5 - 2.5 = -4.5

Then, use the pythagorean theorem on the absolute value of x and y (disregard the negative signs).

c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
= sqrt(2^2 + 4.5^2)
= sqrt(4 + 20.25)
= sqrt(24.25)
= 4.9
 
  • #5


I would approach this problem by first understanding the concept of vector addition. When adding vectors, we need to take into account both the magnitude and direction of each vector. In this case, we have three vectors (S, T, and U) and we want to find the magnitude of the resultant vector, which is the vector that represents the sum of these three vectors.

To find the magnitude of the resultant vector, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we can consider each vector as one side of a triangle, and the resultant vector as the hypotenuse.

To apply the Pythagorean theorem, we first need to find the x and y components of the resultant vector. We can do this by adding the x components of the three given vectors together, and then adding the y components together. In this case, we get:

Rx = -3.5 + 0 + 5.5 = 2
Ry = 4.5 - 6.5 - 2.5 = -4.5

Next, we can use these components to calculate the magnitude of the resultant vector using the formula:

|𝑅| = √(Rx² + Ry²)

Substituting in our values, we get:

|𝑅| = √(2² + (-4.5)²) = √(4 + 20.25) = √24.25 = 4.9

Therefore, the magnitude of the resultant vector S + T + U is 4.9. I hope this explanation helps you understand how to solve this problem. It's always important to understand the concepts behind a problem in order to find the correct solution. If you need further assistance, don't hesitate to ask your teacher or a classmate for help. Good luck!
 

1. What is the definition of "magnitude of the resultant vectors"?

The magnitude of the resultant vectors is the length or size of the combined vector that results from adding two or more vectors together.

2. How is the magnitude of the resultant vector calculated?

The magnitude of the resultant vector is calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the lengths of the other two sides (a and b). In the case of vector addition, the magnitude is equal to the square root of the sum of the squares of the individual vector components.

3. What units are used to measure the magnitude of the resultant vector?

The units used to measure the magnitude of the resultant vector depend on the units of the individual vectors being added together. If the individual vectors have the same units, then the resultant vector will have the same units as well. If the individual vectors have different units, then the resultant vector will have a unit that is a combination of the individual units, such as meters per second (m/s) for velocity.

4. Can the magnitude of the resultant vector ever be negative?

No, the magnitude of a vector is always a positive value. It represents the size or length of the vector, which cannot be negative. If the resulting vector has a negative direction, it is represented by the negative sign in front of the magnitude, but the magnitude itself is always positive.

5. How does the direction of the vectors affect the magnitude of the resultant vector?

The direction of the vectors does not affect the magnitude of the resultant vector. Only the length or size of the vectors and the angle between them determine the magnitude of the resultant vector. The direction of the resultant vector is determined by the direction of the individual vectors and the angle between them.

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