Ways to determine distance between position vectors

[igotoschool123]

Hi everyone please refer to part a) of the question attached.


Initially, when I tried to determine the distance AB, I used b-a, which seemed feasible from the pallelogram rule of addition.
That would mean the distance (rise, run) between A and B is:
run of AB= 2-(-3) = 5, rise of AB = 9-6 = 3
Hence the vector that describes AB is (5,3) which would mean the position vector of the midpoint if (2.5, 1.5)
However, the answer is (-0.5, 7.5)
To find this answer I tried doing a-b which was right
Could someone point out to me why using b-a is incorrect?

Other methods I considered was just finding the midpoint of the two coordinates which didn't work
Thanks

 

[lev888]

which would mean the position vector of the midpoint if (2.5, 1.5)

This is a vector, but not the position vector.

 

[BigBeachBanana]

I tried to determine the distance AB

I would use the distance formula to determine the distance of AB.

 

[Dr.Peterson]

Hi everyone please refer to part a) of the question attached.
View attachment 30741

Initially, when I tried to determine the distance AB, I used b-a, which seemed feasible from the pallelogram rule of addition.
That would mean the distance (rise, run) between A and B is:
run of AB= 2-(-3) = 5, rise of AB = 9-6 = 3
Hence the vector that describes AB is (5,3) which would mean the position vector of the midpoint if (2.5, 1.5)
However, the answer is (-0.5, 7.5)
To find this answer I tried doing a-b which was right
Could someone point out to me why using b-a is incorrect?

Other methods I considered was just finding the midpoint of the two coordinates which didn't work
Thanks

I'd like to see your entire work, rather than just a description of it. The answer is neither b - a nor a - b. The vector you found, (b - a)/2, is AP, where P is the midpoint. They want OP.

You're right that vector AB is (5, 3), and the distance between A and B is the magnitude of that vector; but that is not directly relevant to the question unless you did additional work that you didn't mention. (And in the end there is a much simpler way.)

 

[blamocur]

Hi everyone please refer to part a) of the question attached.
View attachment 30741

Initially, when I tried to determine the distance AB, I used b-a, which seemed feasible from the pallelogram rule of addition.
That would mean the distance (rise, run) between A and B is:
run of AB= 2-(-3) = 5, rise of AB = 9-6 = 3
Hence the vector that describes AB is (5,3) which would mean the position vector of the midpoint if (2.5, 1.5)
However, the answer is (-0.5, 7.5)
To find this answer I tried doing a-b which was right
Could someone point out to me why using b-a is incorrect?

Other methods I considered was just finding the midpoint of the two coordinates which didn't work
Thanks

If you draw either [imath]\mathbf a-\mathbf b[/imath] or [imath]\mathbf b-\mathbf a[/imath] with their tails at the origin you will see that their heads do not lie on AB.

 

[igotoschool123]

I'd like to see your entire work, rather than just a description of it. The answer is neither b - a nor a - b. The vector you found, (b - a)/2, is AP, where P is the midpoint. They want OP.

You're right that vector AB is (5, 3), and the distance between A and B is the magnitude of that vector; but that is not directly relevant to the question unless you did additional work that you didn't mention. (And in the end there is a much simpler way.)

Thank you
Further steps I could've taken from my current working would be to add the vector AP to vector a which could give the resultant position vector OP
That would be:
Midpoint of AB (2.5,1.5) + vector a (-3,6)
= (-0.5, 7.5) which is the textbook answer

Could you point me in the direction of the much simpler way ?

 

[Dr.Peterson]

Thank you
Further steps I could've taken from my current working would be to add the vector AP to vector a which could give the resultant position vector OP
That would be:
Midpoint of AB (2.5,1.5) + vector a (-3,6)
= (-0.5, 7.5) which is the textbook answer

Could you point me in the direction of the much simpler way ?

That's what I presumed you would have done next.

The simpler way is the result of part (b). Have you done that yet, and simplified the result?