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Mathematics: Post your doubts here!

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DudeWithoutName

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Holmes said:
Common perpendiculars??? finding the intersection line of these two planes(other method)
Click to expand...
Ok nevermind that. If you want a plane that is perpendicular to both, then the line of intersection of the two planes must act as a perpedicular to the third plane correct?
basically want to find the equation of that line and then we can proceed from there. We have point A on the line with y coordinate of 2 so lets find its x and y components
x+2+3z=8....x+3z=6
2x-2(2)+z=3....2x+z=7
rearrage the first equation to make x the subject
x=6-3z
substitute x into the second equation
2(6-3z)+z=7
12-5z=7
z=1
x=3
so A: (3,2,1)
Thats one part down. Now we need to find ANY other point on that line so we can figure out its direction. Let us take y=3
x+3+3z=8....x+3z=5
2x-2(3)+z=3....2x+z=9
rearrage the first equation to make x the subject
x=5-3z
substitute x into the second equataion
2(5-3z)+z=9
10-5z=9
z=0.2
x=4.4
so the other point is (4.4,3,0.2)
Let us find the direction of the line then:
[4.4i+3j+0.2k]-[3i+2j+k]=[1.4i+j-0.8k] This is the normal to the plane in question

setting up the cartesian equation of the plane: 1.4x+y-0.8z=[1.4i+j-0.8k].[3i,2j,k]

1.4x+y-0.8z=5.4
1.75x+1.25y-z=6.75
7x+5y-4z=27
 
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DudeWithoutName

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amina1300 said:
https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
part ii) Do we only use sinx for the angle between line and plane?

part iii) The point C lies on the line and is such that the distance between C and B is twice the distance between A and B. Find the coordinates of each of the possible positions of the point C.
(can anyone solve this?)
Click to expand...
The angle between the line and the plane can be thought of as 90-the angle between the normal and the line

First we find the angle between the normal and the line:
(i-3j+4k).(4i-j+5k)=sqrt(1^2+3^2+4^2)*sqrt(4^2+1^2+5^2)cos(theta)
solve for theta
theta=35.2
90-theta=54.8
 
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DudeWithoutName

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amina1300 said:
https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
part ii) Do we only use sinx for the angle between line and plane?

part iii) The point C lies on the line and is such that the distance between C and B is twice the distance between A and B. Find the coordinates of each of the possible positions of the point C.
(can anyone solve this?)
Click to expand...
upload_2018-5-21_1-7-17.png
Writing the second part in chat is far too tedious so i hope this picture is clear. Whats left is putting the two values of t into OC
 
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DudeWithoutName

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amina1300 said:
https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_s16_qp_61.pdf
I can get how Q6 part (a) is done?! It's so confusing :confused::confused::confused: HELP!
Click to expand...
Find the number of ways to arrange the digits 0,1,2,3,4,5,6,7,8,9 into 3 slots. That is 10P3=720
Now we need to take away all that starts with 0 because its less than 100 so we find the number of ways to arrange the digits 1,2,3,4,5,6,7,8,9 into the last 2 slots. This equals the number of instances in which 0 is the first digit and can be calculated by 9P2=72

720-72=648
 
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DudeWithoutName

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amina1300 said:
https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w17_qp_32.pdf
Q1 (ii) Explain, with reference to the diagram, why the trapezium rule may be expected to give a good approximation to the true value of the integral in this case.
WHAT TO WRITE?
Graph on both sides of the y-axis is approximately trapezium shaped?
Click to expand...
That the gradient is roughly constant over that period so the trapezium drawn will have one edge that follows the curve's edge making their areas very similar
 
Holmes

Holmes

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Holmes

Holmes

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253
DudeWithoutName said:
Ok nevermind that. If you want a plane that is perpendicular to both, then the line of intersection of the two planes must act as a perpedicular to the third plane correct?
basically want to find the equation of that line and then we can proceed from there. We have point A on the line with y coordinate of 2 so lets find its x and y components
x+2+3z=8....x+3z=6
2x-2(2)+z=3....2x+z=7
rearrage the first equation to make x the subject
x=6-3z
substitute x into the second equation
2(6-3z)+z=7
12-5z=7
z=1
x=3
so A: (3,2,1)
Thats one part down. Now we need to find ANY other point on that line so we can figure out its direction. Let us take y=3
x+3+3z=8....x+3z=5
2x-2(3)+z=3....2x+z=9
rearrage the first equation to make x the subject
x=5-3z
substitute x into the second equataion
2(5-3z)+z=9
10-5z=9
z=0.2
x=4.4
so the other point is (4.4,3,0.2)
Let us find the direction of the line then:
[4.4i+3j+0.2k]-[3i+2j+k]=[1.4i+j-0.8k] This is the normal to the plane in question

setting up the cartesian equation of the plane: 1.4x+y-0.8z=[1.4i+j-0.8k].[3i,2j,k]

1.4x+y-0.8z=5.4
1.75x+1.25y-z=6.75
7x+5y-4z=27
Click to expand...

Thanks boyz
 
insharah

insharah

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i need help in a recent paper 2017 feb march paper 32
question number 5
any help would be appreciated
thank u in advance;)
 

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