Recent content by petertheta

I get it. so I could descibe the surface as a sphere with a centre... and radius... which I deduce algebraically?

post #13 and #15 suggwsted that this was not possible but anyway... Ok so we have a sphere. Is it this surface then that satisfies the question? No matter what values of A or B. A point M sat on the sphere... will satisfy the orthognality of the two vectors when dotted??

ax - ap -x^2 +xp + by - bq - y^2+yq + cz-cr-z^2+zr = 0 then rearrange to give: x^2 + y^2 + z^2 = a(x-p) + b(y-g) + c(z-r) but I was told I couldn't do this??

I see. Just revising conics but how do i relate this to th points i have? theyre algebraic so none of them "disappear" to form one of the possible conics?

The only way I know how to show something is a sphere is that all points are equal distance from the centre. i think I need more help?

I appreciate your help. the above staement is an equation though isn't it? You are given: \vec{AM}.\vec{MB} = 0 in the question. using your sugested A=(a,b,c) B=(p,q,r) and M=(x,y,z) for the points isn't \vec{AM} = (a-x, b-y, c-z) \vec{BM} = (x-p, y-q, z-r) Hence the inner...

I'm lost. could use parameterization to check something like the volume or surface area to confirm it was a sphere?!?

I could factor into: a(x-p) +b(y-q) +c(z-r) which looks like an equation of a plane...

Ah, If I expand further I get a sphere centred at the origin with radius = (ax-ap+by-bq+cz-cr)^2

OK. So what I get when I take the inner product as you say: (a-x)(x-p) +(b-y)(y-q) +(c-z)(z-r) = 0 Do I expacnd further and rearrange to something?? Thanks

Hi - I'm totally stuck with this question: how to interpret it and tackle it. Any advice woiuld be greatly received! We've not covered anything like this in classes... Let A = \left( x_{A}, y_{A}, z_{A} \right) B = \left( x_{B}, y_{B}, z_{B} \right) be two given distinct points in the...

Thanks for confirming this Mute. i run into a problem further down the line. I get solns at the Stationary Point as x=-4, x = 7, x=-1 but after applying x(t) = x^\ast + \epsilon(t), then expanding and linearizing I end up with a DE in \epsilon that I can't solve. For example. x* = -1 I'm...

Q. Find SP of:\dddot{x} + \ddot{x} + \dot{x} = x^3 -2x^2 - 31x -28 x(t)=x And determine of the solutions as stable or unstable. OK, not seen one like this before. I've done it with 2nd order derivatives and wondered if it was the same. by setting the derivatives to zero and solving the RHS...

I'm afraid I've not covered this before so am at a loss of even how to start this?

I've not seen this method before can you explicitly show me how to proceed? In the question the vectors are the other way around so \vec{v1} = 5\hat{x} + 0\hat{y} and \vec{v2} = 3\hat{x} + 4\hat{y} Thanks