What is the correct magnitude and direction of the vector D and E?

In summary, the conversation revolved around using the component method to determine the magnitude and direction of two vectors, D and E, using given displacement vectors A, B, and C. The student had difficulty finding the correct answer for part B, but after rechecking their work, it was confirmed that their answers were correct. The conversation ended with frustration towards the book's incorrect answer for part B.
  • #1
Frankie715
12
0

Homework Statement


Consider the three displacement vectors

A=(3i-3j) m
B=(i-4j) m
C=(-2i+5j) m

Use the component method to determine (a) the magnitude and direction of the vector:

D= A+B+C and

(b) the magnitude and direction of:

E=-A-B+C

Homework Equations


The Attempt at a Solution



I did A+B+C which resulted in

2i-2j. I put them in the equation to find the magnitude which is

sqrt (2^2+(-2)^2) which resulted in 8. Square root of 8 is 2.82, but the back of the book says the answer is 4.47.

What am I doing wrong?

Thanks for any assistance!
 
Last edited:
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  • #2
Well it seems good

is the answer to (b) also coming wrong?
 
  • #3
Yeah,

For B) I did

arctan(-2/2) which is -45 degrees and the book says its 63.4 degrees
 
  • #4
you are doing part b wrong

its not -2/2

find E again
 
  • #5
cupid.callin said:
you are doing part b wrong

its not -2/2

find E again

Woops, I thought you were referring to the second part of part A to find the direction of the vector. I haven't begun part B yet. I will do it now to see if it matches the back of the book.
 
  • #6
I got a magnitude of 13.4 for part B, but it is saying 8.49. What am I doing wrong?

B) -A-B+C

-6i + 12j

sqrt(36+144)=13.4
 
  • #7
Anyone have any idea what I am doing wrong? I have a test on this tomorrow and would like to know how to do this (If I am doing it incorrectly).

Thanks
 
  • #8
Frankie715 said:
Anyone have any idea what I am doing wrong? I have a test on this tomorrow and would like to know how to do this (If I am doing it incorrectly).

Thanks
Those answers seem right.

Double check the given vectors AND check that the answers are for this problem.
 
  • #9
Dont worry,
your answers are right!Sue That book's writer! :smile:
 

FAQ: What is the correct magnitude and direction of the vector D and E?

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 is typically represented as an arrow pointing from the initial position to the final position of the object.

2. How do you calculate displacement using vectors?

To calculate displacement using vectors, you need to know the initial and final position of the object. Subtract the initial position vector from the final position vector to get the displacement vector. This can be done by breaking down the vectors into their x, y, and z components and performing vector addition.

3. What is the difference between displacement and distance?

Displacement is a vector quantity that represents the change in position of an object, while distance is a scalar quantity that represents the total length of the path traveled by the object. Displacement takes into account the direction of movement, while distance does not.

4. How do you represent displacement vectors graphically?

Displacement vectors can be represented graphically using arrows on a coordinate system. The starting point of the arrow represents the initial position of the object, and the end point represents the final position. The length and direction of the arrow represent the magnitude and direction of the displacement vector, respectively.

5. What are some real-life examples of displacement vectors?

Some real-life examples of displacement vectors include a person walking from one point to another, a car driving from one city to another, a plane flying from one country to another, and a ball rolling down a hill. In each of these scenarios, the displacement vector represents the change in position of the object from its initial to final point.

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