Why Do Vector Components Give Different Displacement Results?

[Acez]

Solving displacement using compoenents

Homework Statement

Homework Equations

I decided to use the horizontal and vertical component method to solve for the displacement of E and got the answer 32.7m [W74.5N] (above). However the answer provided by the question states that the resultant vector E is actually 32m [E25N] (above)

The Attempt at a Solution

Please refer to the above pic.

Am I using the correct approach to solve for the resultant vector E/displacement of E=A-C+2B-D?

Please help

 

[rl.bhat]

Double B, and change the directions of C and D. Redraw the vectors.

 

[Acez]

is the method i am using right though?

EDIT: so first, I have to reverse C and D, redraw vectors and then perform the component calculation from there?

 

[rl.bhat]

In the solution you have taken 8, but it should be 16.
If you reverse the directions of C and D( - C, -D), their x-components of these vectors add up to A adds to

 

[Acez]

thanks i got the right answer now

for future references, could you tell me if the following approaches will be correct?

If i am adding vectors (i.e. A+B+C+D...) i do not need to reverse anything, I will just have to perform components calculation as usual

If I am subtracting vectors (i.e. A-B or 2A-B), I will have to reverse the direction of vectors accordingly and apply any multiplication to a vector (i.e. doubling or tripling) as necessary

 

[rl.bhat]

Yes.

 

[Acez]

thank you very much~!