Finding direction after adding/subtracting vectors?

In summary, the given problem involves finding the vector C-A-B, with a magnitude of 117 and a direction of 71.8° counterclockwise from the +x axis. The attempt at a solution involves using the equation tan^-1 (ry/rx) to find the angle, but there may be a need to subtract 180° depending on a rough sketch of C + (-A) + (-B). Further clarification is needed to fully understand when and why this adjustment is necessary.
  • #1
csgirl504
18
0

Homework Statement



For the vectors given in Fig. 3-32 (|A| = 67.0 and θ = 55.5°), determine the following.

Image for the problem (http://www.webassign.net/giancoli5/3_35alt.gif)

Need to find:

C-A-B

Direction (counterclockwise from the +x axis is positive)



Homework Equations






The Attempt at a Solution




I understand how to find magnitude when adding and subtracting vectors. And I understand that the angle is found by tan^-1 (ry/rx). I got 117 for the magnitude. My rx is -36.5 and my ry is -111.22. So I took the inverse tangent and got 71.8, which is incorrect. I know that sometimes you have to subtract that angle from 180 or something, but I honestly don't know why or when you do that.

If anyone can explain this to me, I would greatly appreciate it!
 
Physics news on Phys.org
  • #2
Welcome to PH Forums.

Make a rough sketch of C + (-A) + (-B) to give you an idea of whether you need to add or subtract 180° .
 

FAQ: Finding direction after adding/subtracting vectors?

1. What is the purpose of adding/subtracting vectors?

The purpose of adding/subtracting vectors is to determine the resultant vector, which represents the combined effect of the individual vectors. This is useful in many scientific fields, such as physics, engineering, and navigation.

2. How do I add/subtract vectors?

To add or subtract vectors, you must first break them down into their components (x and y for 2D vectors, x, y, and z for 3D vectors). Then, simply add or subtract the corresponding components to find the resultant vector's components. Finally, use the Pythagorean Theorem to calculate the magnitude of the resultant vector and use trigonometric functions to find its direction.

3. What if the vectors have different directions?

If the vectors have different directions, you must use trigonometric functions to find the angles between the vectors and then use the Law of Cosines to find the magnitude and direction of the resultant vector.

4. Can vectors be added/subtracted in any order?

Yes, the order in which vectors are added/subtracted does not affect the final result. This is known as the commutative property of vector addition/subtraction.

5. Is there a visual way to add/subtract vectors?

Yes, you can use vector diagrams to visually add or subtract vectors. Draw each vector with its magnitude and direction, and then use the head-to-tail method to find the resultant vector's magnitude and direction.

Similar threads

Finding the magnitude (length) and direction (angle) of a vector
Replies
2
Views
862
Determining vector angle: why do we need to add 180°
Replies
7
Views
7K
Vectors and Two Dimensional Motion
Replies
16
Views
1K
Adding and Subtracting Vectors of Different Directions
Replies
1
Views
1K
Calculate electric force using Coulomb's law (vector components are the struggle)
Replies
3
Views
504
Resultant Vector using Components
Replies
2
Views
2K
Adding Vectors: Understanding Direction and Length
Replies
5
Views
1K
Vector Subtraction: A^{→} - B^{→}
Replies
1
Views
2K
Vector Subtract Given Magnitude
Replies
6
Views
2K
A radar device detects a rocket approaching directly from...
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top