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Mathematics: Post your doubts here!

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Hi I am doing my A2s and I can't do this question please help me!!
oct/nov 10 p.32 q.9
thanks in advance!
 

Maz

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Can someone help me with question 6 May/June 2013 Paper 31 :D
6 i) Seeing that PQ is perpendicular to the plane, PQ is therefore a normal to the plane.

A = midpoint of PQ= (OP+OQ)/2 . (7i+(-5i) +7j+j - 5+k)/2 = i +4j -2k
PQ = q-p = -5i -7i +j-7j +k+5k = -12i -6j+6k

r.n = a.n [equation of a plane]
(xi+yj+zk).(-12i -6j+6k) = (i +4j -2k).(-12i -6j+6k)
-12x-6y+6z = -48
12x+6y-6z = 48

ii) [this would be easier to solve if you make a diagram] [there are two methods of solving this, i'll be showing one]

First find "B"

Since PB is parallel to x-axis its directional vector is "i" = (1 ,0 ,0)
Therefore, The vector equation is=

r=(7i +7j -5k) + t(i)
r=((7+t i)+ 7j -5k)

Put this in the plane equation since PB is intersecting with the plane at B.
12(7+t) +6(7) -6(-5) = 48
t= -9
Put this in the earlier vector equation, the answer is the value of B = (-2,7,-5)

Use the distance equation to the the distance from A to B.
 
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i need help for paper 32 may/june 2013 plzz question 10
plzzz i have an exam 2morrow
 
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The points A and B have position vectors 2i − 3j + 2k and 5i − 2j + k respectively. The plane p has
equation x + y = 5.
(i) Find the position vector of the point of intersection of the line through A and B and the plane p.
(ii) A second plane q has an equation of the form x + by + cÏ = d, where b, c and d are constants.
The plane q contains the line AB, and the acute angle between the planes p and q is 60Å. Find
the equation of q.


this is the question..
 

Tkp

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can some1 help me in may june 12 (32) ques 5
 

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can some1 help me in may june 12 (32) ques 5
dy/dx= e^(2x+y) = e^(2x) * e^y
e^(-y) dy = e^(2x) dx
-e^(-y) = 0.5e^(2x) + c
substitute x=0 y=0
-1 = 0.5 + c c= -1.5
-e^(-y) = 0.5e^(2x) - 1.5
e^(-y) = -0.5e^(2x) + 1.5
-y = ln(3-e^(2x)/2)
y = ln(2/(3-e^(2x))
 
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Tkp

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dy/dx= e^(2x+y) = e^(2x) * e^y
e^(-y) dy = e^(2x) dx
-e^(-y) = 0.5e^(2x) + c
substitute x=0 y=0
-1 = 0.5 + c c= -1.5
-e^(-y) = 0.5e^(2x) - 1.5
e^(-y) = -0.5e^(2x) + 1.5
-y = ln(3-e^(2x)/2)
y = ln(2/(3-e^(2x))
thnks
 

Maz

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Hey, could someone please post notes for complex numbers and vectors. Especially complex- i'm more or less lost... Please...:(
 
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