This discussion is now closed.

Check out other Related discussions

Hard P3 Vectors Question

There's a hard question in Review Exercise 2 on vectors, its question 37 and I can't do part c. I've copied out the relevant bits of info for those who don't have the book, please can someone help.

Thanks

37. OA = 7i + 3j + 8k

With centre O and radius OA a circle is drawn to cut the line L at points A and C. (The straight line L passes through A and B).

Determine the position vector of C.

Thanks again

Reply 1

JamesF

I think we need some more info, what is B??

Reply 2

Morgan

Crap, sorry I forgot to put it in.

OB = 5i + 4j + 6k

Reply 3

Mysticmin

I'm not going to do it, as I haven't done parts a) and b) but the magnitude of vector OC has to be equal to the radius of the circle right? I'm guessing when you equate equations for magnitude, you'll get a quadratic, which solves to given the point of A so you know what c is?

P.s. gimme the answers to a and b I'll try c) :tongue:

I should do all of it, but it's too much effort.

Reply 4

Morgan

Well part (a) is a show that, which is irrelevant and the answer to b is 2, the value of lambda that makes OP perpendicular so thats worthless too :tongue:

.

I tried that method but the whole three dimensions thing is confusing me, along with the fact that I haven't actually formally been taught P3, though we came across something like this with conics in P5 methinks.

Reply 5

JamesF

I get C = (-5, 9, -4).

Reply 6

JamesF

I get C = (-5, 9, -4).

I wrote out all the working, and then the server was busy, so it disappeared :mad:

Basically, the point in between A and C will be perpendicular to the line L. C lies on L, so you can write it as
C = (7,3,8) + t[-2,1,-2].

So A+C will be perpendicular to L
[-2,1,-2] . A+C = 0, expand and solve.

Reply 7

musicbloke

Morgan

the value of lambdaQUOTE]

you think of it like a sheep?

MB

Reply 8

Mysticmin

ok |OC| = |OA| as this is the distance from the point the edge the circle cuts the line and O is the centre.

|OA| = √122

L = 5i + 4j + 6k + a(-2i + j -2k)

so (5 - 2a)² + (4+a)² + (6-2a)² =122

Open up and solve :smile:

(I then did)

25 - 20a +4a² + 16 + 8a + a² + 36 -24a + 4a² = 122
9a² - 36a + 77 - 122 = 0
9a² - 36a - 45 = 0
a² -4a - 5 = 0
(a-5)(a+1) = 0

So C is (-5, 9, -4)

Reply 9

Morgan

Thats the right answer James thanks, and I'm sorry I can't reply quickly my connetion so damned screwy today.

Thanks Mysticmin too, I'll try doing it myself now.

Musicboy - I hope you're not implying that I'm screwing mathematical symbols, that would mean I'd be cheating on my dear sheep.

Reply 10

Mysticmin

Morgan

Posting maths symbols on the internet takes such a long time, we should have a comprehensive click button :mad:

wouldn't hurt for my computer to learn some telepathy as well. Think I should customise my keyboard so I can press a button for a sq root and stuff.

Reply 11

Morgan

Mysticmin

Posting maths symbols on the internet takes such a long time, we should have a comprehensive click button :mad:

wouldn't hurt for my computer to learn some telepathy as well. Think I should customise my keyboard so I can press a button for a sq root and stuff.

Yeah I know what you mean, they could just pop something under the smilies or something, seeing as a lot of people talk about maths questions on here. For me maths itself is getting awfully tedious, I've tried a P3 Paper today and barring a heap of stupid errors, I've been right all the way through, i just hope its a hard paper it'll make it easier for us Further Mathers, I know I always make stupid little mistakes.

Reply 12

Mysticmin

Morgan

Me too, all the time. Ironic isn't it, I get higher in P4 than I do in P1

Reply 13

Morgan

Dang!!!! Every single time I try to reply something screws up.

Thanks for the full solution Mysticmin. Totally get you on the P4 thing, P2 is really just a mesh of lots of totally seperate subjects and P3 is tiresome, somehow its like a mistake-minefield.

PS Sorry I couldn't reply to your PM, I did try, but thats even harder to do than this.

:cool: