Find the line of intersection of the planes 𝑥+𝑦−2𝑧=2 and 2𝑥−𝑦+𝑧=1.

Answer 1

Let add these equations: 3x - z = 3. So z = 3x - 3. We put this in second equation: 2x - y + 3x - 3 = 1, so

y = 5x - 4. Now let x = t, then y = 5t - 4, z = 3t - 3. This is parametric equation of line: x = t, y = 5t - 4, z = 3t - 3.

To get symmetric equation: x/1 = (y + 4)/5 = (z + 3)/3