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Vectors Question Help

Any help on this one:

Given that point A has the position vector 4i + 7j and point B has the position vector 10i + qj, where q is a constant, find

a) the vector AB in terms of q

b) Given further that |AB| = 2√13, find two possible values of q showing detailed reasoning in your working

Thanks :smile:
because the vectors are 2 dimensional it is a good idea to draw a picture.
Original post by AtomicCow
Any help on this one:

Given that point A has the position vector 4i + 7j and point B has the position vector 10i + qj, where q is a constant, find

a) the vector AB in terms of q

b) Given further that |AB| = 2√13, find two possible values of q showing detailed reasoning in your working

Thanks :smile:


AB is just OB-OA

For second part, just take the magnitude of the above, make it equal the specified length, solve the equation for two values of q.
Reply 3
I understand the first bit
AB = AO + OB
= -(4i + 7j) + 10i +qj
=6i - 7j + qj

and I think I'm just being stupid but what from there
Original post by AtomicCow
I understand the first bit
AB = AO + OB
= -(4i + 7j) + 10i +qj
=6i - 7j + qj

and I think I'm just being stupid but what from there

Read my post - find the magnitude and carry on.

Factor the j component first so you’d avoid confusion
Reply 5
Original post by RDKGames
Read my post - find the magnitude and carry on.

Factor the j component first so you’d avoid confusion


Ok I've got 2√13 = √q^2-14q+85

Is that somewhere on the right lines?
(edited 6 years ago)
Original post by AtomicCow
Ok I've got 2√13 = √q^2-14q+85

Is that somewhere on the right lines?


Should be 85, not 80, but yes that's right so far.
Reply 7
Original post by AtomicCow
Ok I've got 2√13 = √q^2-14q+85

Is that somewhere on the right lines?


And I've got -3 and -11 which I think it right.

Thanks :smile:
Original post by AtomicCow
And I've got -3 and -11 which I think it right.

Thanks :smile:


Swap the signs then you're correct. Explore where your error lies.
Reply 9
Original post by RDKGames
Swap the signs then you're correct. Explore where your error lies.


Oh yeah, It's just because I had (q-3)(q-11) and forgot to make the brackets equal to zero
can someone write the method out please I'm struggling to follow
Reply 11
how did you get that?
Reply 12
Original post by AtomicCow
Ok I've got 2√13 = √q^2-14q+85

Is that somewhere on the right lines?



how did you get this?

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