Question

Find the parametric equation and symmetric equation for the line of intersection of the planes x + 2y + 3z = 1 and x - y + z = 1?

Answer 1

To find the parametric equation and symmetric equation for the line of intersection of the planes x + 2y + 3z = 1 and x - y + z = 1, set up the system of equations, solve the system, and write the equations.

Step-by-step explanation:

To find the parametric equation and symmetric equation for the line of intersection of the planes x + 2y + 3z = 1 and x - y + z = 1, we can use the method of solving systems of linear equations.

Step 1: Set up the system of equations:

x + 2y + 3z = 1

x - y + z = 1

Step 2: Solve the system of equations to find the values of x, y, and z.

Solving the system of equations gives us x = 1, y = 0, and z = 0.

Step 3: Write the parametric equation and symmetric equation.

The parametric equation is:

x = 1 + t

y = 0

z = 0

The symmetric equation is:

(x - 1)/1 = (y - 0)/0 = (z - 0)/0