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june 2012 p3 9707 last question .
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june 2012 p3 9707 last question .
applepie1996
We have to find the point p where the perpendicular distance to the two planes is same.
first we will for an equation the way the paper gave.
therefore
for plane m
|x+2y-2z-1|/sqrt((1^2) + (2^2) + (-2^2) = |x+2y-2z-1|/3 [P.S, sqrt is square root]
for plane n
|2x-2y+z-7|/sqrt((2^2)+(-2^2)+(1^2) = |2x-2y+z-7|/3
since you are finding a point where both distance is same , therefore.
|x+2y-2z-1|/3 = |2x-2y+z-7|/3 (3 can be cancelled both sides)
=
|x+2y-2z-1| = |2x-2y+z-7|
now we will sub the line values in the equation.
the x component (1+2t) [P.S, t is lamda ]
the y comp. (1+t)
the z comp. (-1+2t)
therefore.
| (1+2t) +2 ( 1+t) -2(-1+2t) -1 | = |2(1+2t) - 2(1+t) + (-1+2t) - 7 |
simplifying it you get
|4| = |-8+4t|
now to solve modulus, we do squaring method
16 = 64-64t+16t^2
simplify
2 = 8 - 8t +2t^2
2t^2 - 8t + 6 = 0
solve it and get
t = 3 or t= 1
when t=3 the position of point is [P.S, u do this by sub t value in line equation)
(7, 4, 5) => OA
when t = 1 the position of point is
(3, 2, 1) => OB
BA (or AB, same thing) = OA - OB
= (4 , 2, 4)
now find the mod
sqrt(4^2 + 2^2 + 4^2)
= 6
I dint do every step in detail, (very long) if u dont get any step, just ask. [Pray for me please.]
Thanks genious InshaAllah u'll ace the exams with huge success XDThis is only the last part, I think:
Thanks genious InshaAllah u'll ace the exams with huge success XD
What i got is this (doesnt seem correct though)http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w09_qp_31.pdf
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w09_ms_31.pdf
Q7iv) How do we show the shading for this: 0 < arg(z − u) < 1/4 π ?
Now that is where I got wrong ! Thanks again! Yup, you said it correct! Now if I made it from 1, the answer will correct. (i think) Jazaki Allah khairan!Actually no hold on... the perpendicular bisector is at x=1, so we have to shade to the left of it... you shaded to the left of x=2
check thishttp://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_32.pdf
PhyZac Could you tell me what you did in Q8ii) ?
I didn't exactly understand the question
Check this! This is the syllabus, go to Pure 3, and you will find the stuff that might come in exam!Help how to know wats coming of the exam
karim in math every question will include every part of the syllabus..nothing will be missed in math all the chapters in the book will be involved in the questions. like literally every chapter!!Help how to know wats coming of the exam
Now that is where I got wrong ! Thanks again! Yup, you said it correct! Now if I made it from 1, the answer will correct. (i think) Jazaki Allah khairan!
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w07_qp_6.pdf
littlecloud11
I have prob in no 7.. cant understand what they did in the markscheme
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