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# P3 Help Thread watch

1. There seems to be a lot of P3 questions coming up, so I thought I'd start a thread where everyone can help each other. I'm pretty nifty on the more pure side of things and will be glad to help whenever I can get online, but for now I'll start with a problem I've got on vectors.

Review Exercise 2 Question 33

Referred to a fixed origing O, the points A and B have position vectors (5i-j-k) and (i-5j+7k) respectively.

(a) Find an equation of the line AB. (Simple enough, got the answer correct.)
(b) Show that the point C with position vector (4i-2j+k) lies on AB. (Simple as well.)
(c) Show that OC is perpendicular to AB. (Easy also.)
(d) Find the position vector of the point D, where D (does not equal) A, on the line AB such that the modulus of OD is equal to the modulus of OA. (Any help greatly appreciated, can't think of how to do it.)

Thanks.
2. (Original post by Morgan)
Review Exercise 2 Question 33

Referred to a fixed origing O, the points A and B have position vectors (5i-j-k) and (i-5j+7k) respectively.

(a) Find an equation of the line AB. (Simple enough, got the answer correct.)
(b) Show that the point C with position vector (4i-2j+k) lies on AB. (Simple as well.)
(c) Show that OC is perpendicular to AB. (Easy also.)
(d) Find the position vector of the point D, where D (does not equal) A, on the line AB such that the modulus of OD is equal to the modulus of OA. (Any help greatly appreciated, can't think of how to do it.)

Thanks.
You know that OC is perpendicular to line AB from part (c), so C must be the point on AB closest to the origin. Therefore, a point in the other direction from C of the same magnitude as |AC| will also have |OA|=|OD|
3. Thanks Zaphod, for some reason I just assumed the line AB went through the origin which it clearly doesn't, I've got the right answer now though. Thanks.
4. was the answer 3i -3j + 3k, just out of interest?
5. Yeah thats the right answer (I didn't post the answers before in case someone wanted to do it).

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