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is (b - a) and (a - b) the same in vectors ??

So in my book they wrote
b - a
but I wrote a - b and I was wondering if they are both considered to be the same?:smile:

They're the same in magnitude, but opposite in direction.
Original post by Adorable98
So in my book they wrote
b - a
but I wrote a - b and I was wondering if they are both considered to be the same?:smile:



No they are not the same because you wrote b as minus which it isn't as you travel in the direction the arrow is pointing in which means it is positive. Therefpre it can only be written as b-a or -a+b. Hope this helps!
Reply 3
Original post by Speedbird129
No they are not the same because you wrote b as minus which it isn't as you travel in the direction the arrow is pointing in which means it is positive. Therefpre it can only be written as b-a or -a+b. Hope this helps!


Okay then, so why is the answer b - a not a - b? :s-smilie:
Original post by Adorable98
Okay then, so why is the answer b - a not a - b? :s-smilie:


It is not a-b because to get from the start of the red dashed line to the end you have to travel along b in the direction the arrow is pointing, therefore b is positive. Then you travel down b in the opposite direction to the arrow, therefore it is negative. This is why b is positive and a is negative and therefore it is incorrect the other way round. Hope this helps!
(edited 7 years ago)
Original post by Speedbird129
It is not a-b because to get from the start of the red dashed line to the end you have to travel along b in the direction the arrow is pointing, therefore b is positive. Then you travel down b in the opposite direction to the arrow, therefore it is negative. This is why b is positive and a is negative and therefore it is incorrect the other way round. Hope this helps!


Sorry, my mistake you travel down b and then a in the opposite direction to the arrow, therefore a is negative.
Reply 6
Original post by Speedbird129
Sorry, my mistake you travel down b and then a in the opposite direction to the arrow, therefore a is negative.


I still don't get it? :s-smilie:
Original post by Adorable98
I still don't get it? :s-smilie:


Is this for A-level?
Original post by Adorable98
I still don't get it? :s-smilie:


b-a, on the diagram, is essentially moving from right to left (moving by vector b, then in the opposite direction of vector a). a-b ( a-b = -(b-a): moving by vector a, then moving in the opposite direction of vector b) is the vector moving from left to right.
Basically if you move in the direction that the arrow is pointing in, the letter has to be positive, therefore as you are moving through b in the direction that the arrow is pointing, b must be positive, not negative.
Original post by Middriver
Same size different directions image.jpg


Oh I see now!! Thank you!! :biggrin:
Original post by Speedbird129
Basically if you move in the direction that the arrow is pointing in, the letter has to be positive, therefore as you are moving through b in the direction that the arrow is pointing, b must be positive, not negative.


Original post by oniisanitstoobig
b-a, on the diagram, is essentially moving from right to left (moving by vector b, then in the opposite direction of vector a). a-b ( a-b = -(b-a): moving by vector a, then moving in the opposite direction of vector b) is the vector moving from left to right.


Thank you!!! :h::h:
Original post by Adorable98
Oh I see now!! Thank you!! :biggrin:


No worries.
Thanks for the reps. Hope you understand now and is this for A-level?
Original post by Speedbird129
Thanks for the reps. Hope you understand now and is this for A-level?


Yep!! C4 vectors:smile:
Original post by Adorable98
Yep!! C4 vectors:smile:


Ok, I probably wasn't the best person to help as I am doing my GCSE's now but I would believe the basic principles are the same. Good luck in your studies and exams!

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