Question

Find a parametrization of the line in which the planes x + y + z = -6 and y + z = -8 intersect.

Find the parametrization of the line. Use a point with z = 0 on the line to determine the parametrization.

Answer 1

L(x,y) = (2,-8,0) + (0,-1,1)*t

Explanation:

for the planes

x + y + z = -6 and y + z = -8

the intersection can be found subtracting the equation of the planes

x + y + z - ( y + z ) = -6 - (-8)

x= 2

therefore

x=2

z=z

y= -8 - z

using z as parameter t and the point (2,-8,0) as reference point , then

x= 2

y= -8 - t

z= 0 + t

another way of writing it is

L(x,y) = (2,-8,0) + (0,-1,1)*t