for d)

I did |AP|:|PB|

sqrt3^2+5^2+4^2=sqrt50

sqrt6^2+10^2+8^2=sqrt200

1:2

That´s the safe way to do d). The one I had in mind was recognizing that the line equation in a) was constructed in a way that C(0) = A, C(1)=B, C(0.5) = "middle of AB" and so on. So since you had P on 1/3 of AB the ratio must be (1/3):(2/3) = 1:2.

How did you come about substituting 0 and 1 into C(x)?

In principle, C(t) is simply an equation with one real valued variable. You can put in anything you want. I simply wanted to show you that the line equation C(t) in part a) was constructed in a way that makes the solution to your last question easy to obtain.

Okay I understand. Thank you I hadn't thought of it in that way, that's why.

Vectors are very badly explained in all the books i have. Funnily enough, my exam paper will have 8 questions on 6 topics, and invariably vectors is the one holding the most points.

Now that you have enlightened me i see how the methods are really quite simple. It's just knowing how to apply them to other questions.

 

Would you suggest a sourse ie book with similar vector methods for me ?

Thanks again