QUESTIONS - ANSWERS - VECTORS - 3D GEOMETRY

QUESTIONS - ANSWERS - VECTORS - 3D GEOMETRY
Find the equation of the plane=P SAY, containing the line L1, and parallel to the line L2, where:
L1: (x,y,z) = (-2,-1,1)(Q SAY) + t (-3,0,2).
L2: is the intersection of the planes 2x-2y-3z=-5 and 1x-3y-3z=-3
Write your answer in the form -4x+By+Cz=D, and give the values of B, C and D as your answer.
EQUATION OF P THROUGH Q IS
A(X+2)+B(Y+1)+C(Z-1)=0..............................1
DRS OF NORMAL ARE A,B,C.........NORMAL PERPENDICULAR TO L1
-3A+2C=0........A=2C/3 ...............2
IF DRS OF L2 ARE L,M,N THEN
2L-2M-3N=0...............3
L-3M-3N=0.................4
|-2,-3|
|-3,-3|=6-9=-3
|-3,2|
|-3,1|=3
|2,-2|
|1,-3|=-4
L:M:N=-3:3:-4
HENCE
-3A+3B-4C=0...................5
-3*2C/3 +3B-4C=0
3B=6C
B=2C
A=2C/3.....OR.....TAKING C = 6....A=4,B=12
EQN OF PLANE IS
4(X+2)+12(Y+1)+6(Z-1)=0
-4X-12Y-6Z=14