# Find parametric equations for the line which is the intersection of the planes with equations x+y+z=1 x-y+2z=0

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by mrambabu1600

2014-11-22T03:42:10+05:30

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The equations of two planes are

x + y + z = 1            and    x - y + 2 z  =0

perpendiculars to these planes are given by the vectors :

( 1, 1, 1 ) or i + j + k             (1, -1, 2 )  or  i - j + k

cross product of these two vectors :

- i X j + i X k + j X i + j X k + k X i - k X j  =  2 i   + 0 j  - 2 k  or (2, 0, -2)

Let z = 0,  then solving  x + y +z = 1 and x - y +2 z = 0  gives,
(1/2 , 1/2, 0) is a point on both planes.

Equation of the line intersection of both planes and parallel to (2, 0 , -2) is:

x = 1/2 + 2 t,         y = 1/2 + 0 t     z = 0 + -2 t
or  x = 1/2 + 2 t   ,  y = 1/2  , z = -2 t

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