# Finding the Displacement Vector from 3 Given Vectors

• fortifymagicka
In summary, the physics teacher has given a student a trigonometry problem involving vectors to find a displacement vector. The student is not sure how to go about the problem and is seeking help. The student has attempted to solve the problem but is not sure where to go from there. The student thanks the physics teacher for their time and asks for more help in the future if needed.
fortifymagicka
My physics teacher has given me a worksheet with several problems involving trigonometry to find a displacement vector from a set of given vectors. Since this is my first year in physics, I feel out of my element and would really appreciate any help or direction given to me on how to go about this problem. It is as follows:

"A car travels at 65 km/hr for 30 minutes SSW, then 38 km/hr for 45 minutes SW, then 50 km/kr for 25 minutes due W. What is the car's displacement? What is your total distance?"I am aware that in order to find the total displacement, you must calculate the distance traveled for each vector and then add them together. I have done that, already.

I have attempted to put the vectors together "tip-to-tail", but since the tips of the vectors face west, I have sketched a shape where a "parallelogram" is not formed. My physics teacher only showed brief examples of problems where the three vectors can be connected by a displacement vector to form a figure similar to that of a parallelogram. (i.e. you travel 117 km ENE, then 95 km SE, then 298 km SSW. What is your displacement & total distance?)

Maybe I am just setting the problem up wrong? I've been working on manipulating the vectors to make said shape, but I feel as if that would just alter the displacement from the origin and not give me the correct answer.

I am not sure where to go from here, and would really appreciate the help since I'm not getting the information needed in class. I accept full responsibility for my confusion, however. Perhaps I'm just over-thinking this "simple" problem?

Thank you in advance.

The parallelogram applies when you are adding two vectors. If you are adding more than two, either deal with them two at a time (add two and get a resultant, then add the next vector to that resultant, and so on), or, break all the given vectors down into their individual components at the start and sum the like-components all at once. Combine the resulting component sums into a final resultant vector.

gneill said:
The parallelogram applies when you are adding two vectors. If you are adding more than two, either deal with them two at a time (add two and get a resultant, then add the next vector to that resultant, and so on), or, break all the given vectors down into their individual components at the start and sum the like-components all at once. Combine the resulting component sums into a final resultant vector.

I tried this, then asked my physics teacher for some extra help and I ended up not needing it since I got the right answers. Thank you very much for your time, it's really appreciated!

## 1. What is a displacement vector?

A displacement vector is a mathematical representation of the change in position of an object. It has both magnitude (length) and direction, and can be represented graphically as an arrow pointing from the initial position to the final position of the object.

## 2. How do I find the displacement vector from 3 given vectors?

To find the displacement vector from 3 given vectors, you can use the parallelogram law of vector addition. Draw the three vectors on a coordinate plane, and then draw a parallelogram using the initial and final points of the three vectors. The diagonal of the parallelogram represents the displacement vector.

## 3. Can I use the triangle law of vector addition instead?

Yes, you can also use the triangle law of vector addition to find the displacement vector. This method involves drawing the three vectors on a coordinate plane and connecting the initial and final points of the vectors to form a triangle. The displacement vector is then represented by the third side of the triangle.

## 4. Are there any other methods for finding the displacement vector?

Yes, there are other methods for finding the displacement vector, such as using trigonometric functions and the dot and cross product of vectors. However, the parallelogram and triangle laws are the most commonly used methods for finding the displacement vector from three given vectors.

## 5. What are some real-life applications of finding the displacement vector?

Finding the displacement vector is useful in various fields, such as physics, engineering, and navigation. It can be used to calculate the motion of particles, determine the distance and direction traveled by vehicles, and plan routes for airplanes and ships. It is also used in sports, for example, to analyze the trajectory of a ball in motion.

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