Calculating Magnitudes and Ratios of Position Vectors on a Line

[pavadrin]

Points A, B and C lie on the line r = 2i + 3j + λ(i + 4j) and have position vectors given by λ=-1, λ=1 and λ=2 respectively.
Find a) AB
b) AB:BC
The answer for part a is the square root of 17 (in exact form) however I keep getting the suare root of 20.
Here is what I am doing:
OB = 3i – j and OC = 5i – 5j
BC= BO + OC
BC= -(3i – j) + (5i – 5j)
BC= 2i – 4j
Therefore the magnitude of BC = square root of 20
As for part b, I’m not sure what it’s asking me to do
Thanks
Pavadrin

 

[Curious3141]

Points A, B and C lie on the line r = 2i + 3j + λ(i + 4j) and have position vectors given by λ=-1, λ=1 and λ=2 respectively.
Find a) AB
b) AB:BC
The answer for part a is the square root of 17 (in exact form) however I keep getting the suare root of 20.
Here is what I am doing:
OB = 3i – j and OC = 5i – 5j
BC= BO + OC
BC= -(3i – j) + (5i – 5j)
BC= 2i – 4j
Therefore the magnitude of BC = square root of 20
As for part b, I’m not sure what it’s asking me to do
Thanks
Pavadrin

I don't get it. The first part is asking for the magnitude of AB, yet you seem to be working out the magnitude of BC?

In any case, your position vectors for both OB and OC are wrong. How did you do that? All you have to do is substitute the given values of λ into the equation to get the position vectors.

Maybe I think it'd be better if you showed full working on how you get OA, OB and OC, because the first part is simple algebra.

Part b) AB:BC is simply asking you to find the ratio between the lengths of the two line segments AB and BC. All you have to do is find |AB|, |BC| then take the ratio (I get two).

 

[pavadrin]

sorry, it was meant to say the magnitude of BC, not AB. I have solved this now, so there's no need to worry bout it. As for part b), thanks for clearing that piont up, i should be able to work from here, otherwise i will re-post asking fro help
thanks