Question

Consider the planes x_1 + x_2 + 3x_3 =4 and x_1 + 2x_2 + 4x_3 = 5 in r3 find parametric equations for the line of intersection of these two planes

Answer 1

You can solve for x and y in terms of z, then let z take on the value of the parameter.

Subtracting the first equation from the second, you get

... x_2 +x_3 = 1

Subtracting that from the first equation gives you

... x_1 +2x_3 = 3

Let x_3 = t. Then your parametric equations are ...

$x_1=3-2t\\x_2=1-t\\x_3=t$