Qualification > Math

Need HELP on CIE Maths P1/P3/M1

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The SMA:
Hey guys, i need some help on P3 M/J 2003 Q9
and on P3 M/J 2002 Q8.

Both are Vectors questions and i found it hard + confusing to solve.
I hope someone can help me step by step  :)

astarmathsandphysics:
mj 2003 q9
The angle between the planes is the angle between the normal
normal to x+2y-2z=2 is (1,2,-2) and normal to 2x-3y+6z=3 is (2,-3,6)
For b see http://astarmathsandphysics.com/a_level_maths_notes/C4/a_level_maths_notes_c4_finding_the_line_of_intersection_of_two_planes.html

astarmathsandphysics:
for mj 2002 p3 a) first you have to find the line passing through A and B
r=A +t(B-A) =(1,0,1) +t(3,-1,2)
Then follow this method
http://www.astarmathsandphysics.com/a_level_maths_notes/C4/a_level_maths_notes_c4_finding_the_point_of_intersection_of_a_line_with_a_plane.html

The SMA:
I have done the mj 2003 q9 and the mj 2002 q8 (i) correctly.
But I still can't get the answer for q8 part (ii).

Since the new plane contains line l and it is perpendicular to p
[and by letting normal of the new plane to be (ax+by+cz)],

(3,-1,2).(a,b,c)=0 and (1,3,-2).(a,b,c)=0

I came up with two equations ; 3a-b+2c=0 --(1) and a+3b-2c=0 --(2)
and when I solve them simultaneously,all interms of b, i got (a,b,c) = (-1/2b,b,5/4b)
and then here is where i stucked. I need more help on here.

By the way, Thank you very much astar for your help . What an interesting site you have there!
It is very very helpful for me :)

astarmathsandphysics:
I dont understand your method. Home in few hours

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