# Solving Displacement Vectors A & B: Find A+B

• chocolatelover
In summary, the problem given involves finding the result of adding two vectors, A and B, with magnitudes of 3 m and an angle of 30° formed by the positive x-axis. The solution involves finding the components of the vectors in the x and y directions, adding them, and then converting back to a magnitude and direction. The magnitude of A+B is 6 and the angle is 179.4°, while the magnitude of A-B is also 6 but the angle is 0°. The solution provided in the conversation did not take into account the direction of the vectors, resulting in incorrect answers.
chocolatelover

## Homework Statement

Vector A is 3 m and vector b is 3m. The angle formed by the positive x-axis is 30°. Find A +B

## The Attempt at a Solution

Does this look correct?

i=3cos30
j=3sin30

Vector A+B=(3cos30 +3cos30)+(3sin30+3sin30)
=8.20

magnitude=square root((3cos30 +3cos30)^2+(3sin30+3sin30)^2)
=square root(27+9)=6

theta=tan-1(3sin30+3sin30)/(3cos30+3cos30)=77.55

and if it were vector A-B, the only difference would be that you would take (3cos30+3cos30)+(-3sin30-3sin30) and the magnitude would be square root of (3cos30+3cos30^2)+(-3sin30-3sin30)^2 right?

Thank you very much

Last edited:
chocolatelover said:
The angle formed by the positive x-axis is 30°.

I have no Idea what you mean by this.

Sorry.The angle formed by the two vectors on the positive x-axis is 30°. Can you tell me if I did this correctly? Would the magnitude of vector A+B be the square root of (3cos30+3cos30)^2+(3sin30+3sin30)^2
=6
angle=3sin30+3sin30/3cos30+3cos30=179.4

Would the magnitude of A-B be:
square root of (3cos30+3cos30)^2+(3sin30+3sin30)=
6

angle=179.4

But they shouldn't be the same, right? Do you see where I went wrong?

Thank you

Last edited:
That still doesn't tell me where A and B point.
The magnitude of A+B can only be 6 if A and B point in the same direction however, and then of course A+B would have the same direction as A And B and then A-B would be the 0 vector, so your answer can't be right.
The easiest way to do this is to compute the components of A and B in the X and Y directions, then add them, and then convert back to a magnitude and direction.

Thank you very much

Regards

## 1. What is the concept of displacement vectors A and B?

The concept of displacement vectors A and B is based on the idea of using vectors to represent the movement or displacement of an object in space. Displacement vectors are used to describe the distance and direction of an object's movement from its starting point to its ending point.

## 2. How do you find the result of adding displacement vectors A and B?

To find the result of adding displacement vectors A and B, you need to use vector addition. This involves adding the horizontal components of the vectors and the vertical components of the vectors separately, then combining them to find the resultant vector. The magnitude and direction of the resultant vector can be found using trigonometric functions.

## 3. What is the importance of solving displacement vectors A and B?

Solving displacement vectors A and B is important in understanding and accurately describing the movement of objects in space. It allows us to calculate the total displacement of an object and determine its final position, which is useful in many scientific and engineering applications.

## 4. Can displacement vectors A and B be subtracted?

Yes, displacement vectors A and B can be subtracted using the same principles of vector addition. Instead of adding the components, you would subtract them to find the resultant vector. This can be useful in situations where an object may be moving in the opposite direction or returning to its starting point.

## 5. How can I check if my calculation for A+B is correct?

To check if your calculation for A+B is correct, you can use the Pythagorean theorem to calculate the magnitude of the resultant vector. Then, use trigonometric functions to find the direction of the resultant vector. You can also double-check your calculations by drawing a scaled diagram of the vectors and comparing it to your calculated result.

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