Question

Find the set parametric equations of the line of intersection of the planes

x + z = 3 and 2x − y − z = −2.
[A] x = 3 + , y = 4 + 3, z = −
[B] x = 3 + , y = 8 − 3, z = −
[C] x = 3 + , y = 8 + 3, z = −
[D] x = 1 + , y = 3 + 3, z = 2 −
[E] x = 3 + , y = 4 − 3, z = −

Answer 1

The set parametric equations of the line of intersection are: x = 3 - t, y = 2t - 8, and z = t.

Step-by-step explanation:

To find the set parametric equations of the line of intersection of the planes x + z = 3 and 2x − y − z = −2, we need to set up a system of equations using the given planes. Firstly, we can solve the first equation for x in terms of z, yielding x = 3 - z. Then, we substitute this expression into the second equation and solve for y in terms of z, giving y = 2z - 8.

Therefore, the set parametric equations of the line of intersection are: x = 3 - t, y = 2t - 8, and z = t, where t is a parameter.