Help on FP3 Matrix question

Struggling with part b, I've done a few attempts and my answer keeps coming out kind of weird..

Struggling with part b, I've done a few attempts and my answer keeps coming out kind of weird..

3 points:

1) The matrix you used in your working isn't P, or its inverse.
2) Question mentions being transformed by "A". But there is no A: Presumably this is meant to be P
3) You're given the image after transformation, $\Pi_2$, and need to find what is transformed into that. So, you need the inverse matrix.

You're using the wrong matrix. You want to go from the transformed plane to the initial plane, so you need to use the inverse matrix; but you also know P is orthogonal, so the inverse P is the transpose of P - also you seem to be multiplying your matrices out wrong, might want to get that sorted.

Not to be a bother but I responded to the vector question we were talking about yesterday http://www.thestudentroom.co.uk/showthread.php?t=3973217&p=63646553#post63646553

I was trying to do the same method as you suggested but for some reason I mixed my P matrix up :P Anyway, I've tried the question and this is what I got



How can I take my answer further (unless I've gone wrong somewhere)?

Your answer is perfectly correct! Now you just need to state that the plane is $y=0$ and you are done, as x and z can take any values.

Yeah that's the part that lost me! If the question says that the plane is tranformed into another plane surely my answer needs to be in the form of a plane! Also the mark scheme has a different z and x to me but the same y=0 (instead

Think about this: the Cartesian plane you're used to (x-y axes) is just the plane $z=0$, then $x,y$ can take any values you'd like in this plane.

In this case - we have the plane $y=0$ and $x, z$ can take any values since I can choose any $s,t$. So the plane is $y=0$.

Also the mark scheme has a different z and x to me but the same y=0 (instead

I suspect you used a different parametization to the markscheme - which is fine. Can't tell as you've not posted that bit.

Yeah I let x = s, z = t but they mark scheme let y = t instead of z = t!

Yeah, that makes 0 difference and yours is just as valid.

Awesome, thanks!

By the way, have you done M2? Because I can't seem to get this M2 Centre of Mass question correct. I thought all you had to do is 2rsinx/3x which is 12sin60/60 = root3/10 but my answer is incorrect

It's a framework not a uniform lamina.

Got the answer now thanks!
Would you mind spotting where I went wrong on this one