Sketching resultants using vector addition.

[Physics345]

Homework Statement

Given the following diagram, use vector addition to sketch the resultants:
a) u→−2v→
b) 3v→−u→

Homework Equations

The Attempt at a Solution

For this question I am fairly certain that it is correct but for some reason I'm doubting myself. I was wondering if I could get some reassurance and peace of mind by getting someone's confirmation that I am correct.

Note: The questions picture is a lot bigger than it is in the textbook. The diagram I created for a is about 2 times the size of vector v and the diagram i created for question b is about 3 times the size of vector v.

 

[Let'sthink]

Homework Statement

Given the following diagram, use vector addition to sketch the resultants:
a) u→−2v→
b) 3v→−u→
View attachment 222519

Homework Equations

The Attempt at a Solution

For this question I am fairly certain that it is correct but for some reason I'm doubting myself. I was wondering if I could get some reassurance and peace of mind by getting someone's confirmation that I am correct.

View attachment 222520
Note: The questions picture is a lot bigger than it is in the textbook. The diagram I created for a is about 2 times the size of vector v and the diagram i created for question is about 3 times the size of vector v.

You are right. You are having confusion because you think you have added: (-2v)+u in place of {u+(-2v)}. Just for your satisfaction you can draw the diagram for {u+(-2v)} as well but the result will be the same in magnitude and direction as vector addition is commutative A+B = B+A. Similar thing is true for the other diagram.

 

[Physics345]

You are right. You are having confusion because you think you have added: (-2v)+u in place of {u+(-2v)}. Just for your satisfaction you can draw the diagram for {u+(-2v)} as well but the result will be the same in magnitude and direction as vector addition is commutative A+B = B+A. Similar thing is true for the other diagram.

Awesome, that is a great explanation. I love learning new techniques to confirm my solutions, it makes me more confident in my work when I can confirm whether or not it is indeed correct. Also you are spot on about the area of confusion nice job, you explained my confusion better than I.