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Find parametric equations for the line which is the intersection of the planes with equations

x+y+z=1

x-y+2z=0

1
by mrambabu1600

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x+y+z=1

x-y+2z=0

by mrambabu1600

Log in to add a comment

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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

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