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    (Original post by simonli2575)
    Then expand the bracket of (1+x)^1 so the integral could be expressed in terms of I_n and I_{n-1}</span></font><font color="#505050"><span style="font-family: arial">
    Thanks a lot!! That was really frustrating me. I'm worried I wouldn't see something like that in the exam.

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    Did the 2014 paper, forgot what orthogonal matrix meant and q6 was insane.
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    How do you find the line of intersection between 2 planes?

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    (Original post by BP_Tranquility)
    How do you find the line of intersection between 2 planes?

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    You know the line is perpendicular to both of the planes' normal vectors, so d=n1xn2. Find a point on the line by converting the planes to cartesian form, letting any of x, y or z=0 and solving simultaneously for the other two ordinates (this is basically finding x and y when z=0 where the planes intersect, for example)

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    Hmm, only just found this thread. Done all but vectors, and the only real problem seems to be the more complex integrations and loci. Hopefully vectors aren't too difficult.
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    (Original post by Elcor)
    You know the line is perpendicular to both of the planes' normal vectors, so d=n1xn2. Find a point on the line by converting the planes to cartesian form, letting any of x, y or z=0 and solving simultaneously for the other two ordinates (this is basically finding x and y when z=0 where the planes intersect, for example)

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    Do you have to let z=0 or can you let it equal any other constant as well?

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    (Original post by BP_Tranquility)
    Do you have to let z=0 or can you let it equal any other constant as well?

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    Any

    You'd end up with a different point but it's still on the line

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    For the plane equation r.n=a.n, can a be ANY point on the plane?
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    (Original post by Elcor)
    For the plane equation r.n=a.n, can a be ANY point on the plane?
    I'm pretty sure yes.
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    (Original post by simonli2575)
    I'm pretty sure yes.
    I just can't see how a.n is a constant

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    (Original post by Elcor)
    I just can't see how a.n is a constant

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    I think about it like this:
    r.n=a.n comes from (r-a).n=0
    And if you choose another point on the plane for a, r-a is still going to be perpendicular to n
    thus it makes no change.
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    (Original post by simonli2575)
    I think about it like this:
    r.n=a.n comes from (r-a).n=0
    And if you choose another point on the plane for a, r-a is still going to be perpendicular to n
    thus it makes no change.
    Ah good point
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    When proving a line does not meet a plane I imagine it's not enough to show that it's perpendicular to the normal vector, as the line could still lie on the plane.
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    I proved r(L).n=/=a.n which I think is sufficient. Will it always be that the lambdas cancel out in r(L).n (if they do not meet), since no lambda satisfies the equation?
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    (Original post by Elcor)
    I proved r(L).n=/=a.n which I think is sufficient. Will it always be that the lambdas cancel out in r(L).n (if they do not meet), since no lambda satisfies the equation?
    If it's parallel to but does not intersect the plane, then r(L).n will result in an impossible equation, like 2=5.
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    (Original post by simonli2575)
    Did the 2014 paper, forgot what orthogonal matrix meant and q6 was insane.
    Assuming q6 was the loci question; I didn't answer anything beyond part 1 and still got 100 UMS
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    Can someone help me with 14f please? I found a vector which was perpendicular to both planes (as I thought it'd give a parallel vector to plane 1) and then set that equal to the dot product between the new normal vector I found and point A. However, the solution bank instead uses the normal vector for plane A but surely that's a vector which is perpendicular to plane 1 and not parallel?
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    (Original post by BP_Tranquility)
    Can someone help me with 14f please? I found a vector which was perpendicular to both planes (as I thought it'd give a parallel vector to plane 1) and then set that equal to the dot product between the new normal vector I found and point A. However, the solution bank instead uses the normal vector for plane A but surely that's a vector which is perpendicular to plane 1 and not parallel?
    There does not exist a vector perpendicular to both planes, as they themselves are perpendicular. Try visualising it.

    The plane will have the same normal vector as plane 1, as it is parallel. Then just use OA.n

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    How is everyone revising this? Are doing all the review exercise questions in the book and past papers sufficient?
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    What the **** is that June 2009 paper? That was bloody horrific. At least 62/75 was full UMS, which makes me feel slightly less stupid...
 
 
 
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