c4 vectors (again)

hi, i'm really struggling on the last part (f) on question 8 and the guy from YouTube who explains it does an awful job can anyone help please ?

http://pmt.physicsandmathstutor.com/download/Maths/A-level/C4/Papers-Edexcel/January%202014%20(IAL)%20QP%20-%20C4%20Edexcel.pdf

maybe because one unit vector on line L2 is equal to route54 thus we need to make it route24 so we multiply by 2/3 so then does this mean U = 2/3 and if so why

Essentially, you have that right.

$\mu$ will equal +/- 2/3, as appropriate for B1, B2.

The direction vector for l2 has length root(54), so we need to divide it by root(45) to get a unit vector (a vector of length 1) in the same direction as the direction vector for l2.

Then since we need the vector from X along l2, to have length root(24), we multiply by root(24).

thanks for the reply

why does dividing the unit vector by root(45) give a unit vector of size 1, not sure where the value of root(45) comes from?

You mean root(54), not 45.

First off, lets get the terminology correct.

A unit vector is a vector of length 1.

in the lines l1, l2, the vectors multiplied by mu and lambda are direction vectors (they indicate the direction of the lines). They are not unit vectors.

The magnitude of a vector, ai+bj+ck is $\sqrt{a^2+b^2+c^2}$, so if we divide the vector by that to start with, then the magnitude of the resulting vector is 1. Work it through yourself, to check.
This should also indicate to you where the root(54) comes from.

ohh brilliant thanks, the root(45) i was referring to was what you mentioned in your first post "The direction vector for l2 has length root(54), so we need to divide it by root(45) to get a unit vector (a vector o" was that juts a typo i guess?

Yep, sorry. Typo on my part - corrected now.