Find direction from three displacement vectors?

In summary, using the component method, the magnitude of vector D with arrow = A with arrow + B with arrow + C with arrow is 6.09m and the direction is 279 degrees. However, there may have been an error in calculation as the correct answer is different according to WebAssign. Please double check your calculations and make sure all minus signs are correctly placed.
  • #1
amhasque
1
0
Consider the three displacement vectors A with arrow = (-4i hat bold − 3j hat bold) m, B with arrow = (6i hat bold − 8j hat bold) m, and C with arrow = (-3i hat bold + 5j hat bold) m. Use the component method to determine the following.

(a) The magnitude and direction of the vector D arrowbold = A with arrow + B with arrow + C with arrow.
magnitude = 6.09m

direction = ___ I came up with 279 degrees but WebAssign said this was the wrong answer - ( tan-1(6/-1) = -80.5 + 360 = 279 degrees )
-Please let me know what I did wrong. Thanks in advanced!

https://s.yimg.com/hd/answers/i/e9b78a68cdc740ec9325bef84b8802c5_A.jpeg?a=answers&mr=0&x=1411359677&s=c34e6240b312c8a385b3b438af3f4519
 
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  • #2
Show your working - I think you have misplaced a minus sign.
 

1. How do you find the direction from three displacement vectors?

To find the direction from three displacement vectors, you can use the vector addition method. First, draw the three vectors in a coordinate system and label their magnitudes and directions. Then, add the three vectors together using the head-to-tail method. The direction of the resulting vector will be the direction you are looking for.

2. Can you explain the head-to-tail method for finding direction from displacement vectors?

The head-to-tail method is a graphical method used for vector addition. It involves placing the tail of one vector at the head of another vector, and repeating this process for all the vectors involved. The final vector, from the tail of the first vector to the head of the last vector, represents the result of the vector addition. The direction of this final vector is the direction you are looking for.

3. What is the significance of finding direction from three displacement vectors?

Finding direction from three displacement vectors is important for understanding the overall movement or displacement of an object. It can also be useful in navigation and mapping, as well as in physics and engineering calculations.

4. Are there any other methods for finding direction from three displacement vectors?

Yes, another method is using vector components. This involves breaking each vector down into its horizontal and vertical components, then adding the components together to find the resulting vector. The direction of this resulting vector can be determined using trigonometry.

5. How can I check if I have correctly found the direction from three displacement vectors?

You can check if you have correctly found the direction by using the inverse tangent function (tan⁻¹) on the vertical and horizontal components of the resulting vector. The inverse tangent will give you the angle in radians, which you can then convert to degrees to determine the direction.

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