Find A Set Of Parametric Equations For...

Anonymous

From: -
Posts: -
Votes: -
Find a set of parametric equations for theline of intersection of the planes. 3x +2y - z = 7 x - 4y +2z =0

 

Answer No.1

TheBob

From: US
Posts: 24
Votes: 24
Find a set of parametric equations for the line ofintersection of the planes. 3x +2y - z = 7...................P1.......DRS OFNORMAL ARE 3,2,-1 x - 4y +2z=0.......................P2....DRS OF NORMAL ARE 1,-4,2 LET THE DRS OF LINE OF INTERSECTION BE L,M,N. LINE OF INTERSECTION SHOULD BE PERPENDICULAR TO THE NORMAL OF BOTHTHE PLANES.HENCE 3L+2M-N=0.............................................1 L-4M+2N=0..........................................2 2*EQN.1+EQN.2 7L=0 L=0 2M=N............FROM 1....SO DRS ARE 0,M,2M..........OR SAY0,1,2 NOW WE NEED A POINT ON THE LINE A POINT ON THE LINE SATISFIES EQNS. OF BOTH PLANES. LET US TAKE Y=0 3X-Z=7........3 X+2Z=0..................4 2*EQN.3+EQN.4X X=2 Z=-1 HENCE A POINT ON THE LINE IS (2,0,-1) HENCE PARAMETRIC EQN. OF LINE IS (X-2)/0 = (Y-0)/1 = (Z+1)/2 = T OR THAT IS X-2=0 Y=T Z=2T-1

Your Comment/Solution

Post As: Anonymous [Change]
Enter