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FP3 planes question

http://www.ocr.org.uk/Images/57750-question-paper-unit-4727-01-further-pure-mathematics-3.pdf

I'm attempting question 6.

So I've done part 1.

For part 2, I thought that it would be the normal vector in the opposite direction so, (-1,0,2), but it still uses the same normal vector of (1,0,-2). Why is that?
And also for part 3, I'm not to sure how to go about finding the distance, I thought it would be the distance of the second plane - the distance of the first over the magnitude of the normal vector, but when I do it I get the wrong answer :s-smilie:.
Reply 1
Avatar for BabyMaths
BabyMaths
Original post by Music99
http://www.ocr.org.uk/Images/57750-question-paper-unit-4727-01-further-pure-mathematics-3.pdf

I'm attempting question 6.

So I've done part 1.

For part 2, I thought that it would be the normal vector in the opposite direction so, (-1,0,2), but it still uses the same normal vector of (1,0,-2). Why is that?
And also for part 3, I'm not to sure how to go about finding the distance, I thought it would be the distance of the second plane - the distance of the first over the magnitude of the normal vector, but when I do it I get the wrong answer :s-smilie:.


You can multiply the normal by any non-zero scalar and you still have a normal.
Reply 2
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Music99
OP
4
Original post by BabyMaths
You can multiply the normal by any non-zero scalar and you still have a normal.


Yeah, but I mean why is it for part 2, that you use the normal (-1,0,2) which gives a value for d of -3 and not the normal (1,0,-2) which gives a d value of 3, how do you know what one to use?
Reply 3
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BabyMaths
Original post by Music99
Yeah, but I mean why is it for part 2, that you use the normal (-1,0,2) which gives a value for d of -3 and not the normal (1,0,-2) which gives a d value of 3, how do you know what one to use?


First plane

r.<1,0,-2> = d

Substitute a point in the first plane..

<3,4,-1>.<1,0,-2>=d to get d=5. The equation is r.<1,0,-2> = 5.

Second plane

r.<1,0,-2> = d

Substitute a point in the second plane..

<5,1,1>.<1,0,-2>=d to get d=3. The equation is r.<1,0,-2> = 3.
Reply 4
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BabyMaths
It makes no difference, you get x-2z = 3 or -x+2z = -3.
Reply 5
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Music99
OP
4
Original post by BabyMaths
It makes no difference, you get x-2z = 3 or -x+2z = -3.


Ah okay thank you, would you mind helping me with another question?

http://www.ocr.org.uk/Images/59548-question-paper-unit-4727-01-further-pure-mathematics-3.pdf

Question number 6, the last bit.

The first part is r.(1,2,0)=4

The next bit is 74.4 degrees.

So for the last bit, I worked out vector GF which is 4i so then M is 2i?

And then I'm not to sure where to go from there, I know i need to find the point of intersection of the line and plane, but not too sure how.
Reply 6
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aznkid66
1
If I didn't read the previous questions, I would find the vector equation of a line AM with respect to O, then find the cartesian equation of a plane with respect to O using normal OCxOE, then find the common parameters.

But, given the answers to the previous questions, I suspect that you have to draw some similar triangles.
(edited 11 years ago)

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